Revêtements du demi-plan de Drinfeld et correspondance de Langlands $p$-adique

Gabriel Dospinescu; Arthur-César Le Bras

doi:https://doi.org/10.4007/annals.2017.186.2.1

Abstract

Nous décrivons le complexe de de Rham des revêtements du demi-plan de Drinfeld pour ${\rm GL}_2(\mathbf{Q}_p)$. Cette description, conjecturée par Breuil et Strauch, fournit une réalisation géométrique de la correspondance de Langlands locale $p$-adique pour certaines représentations de de Rham de dimension $2$ de ${\rm Gal}(\overline{\mathbf{Q}_p}/\mathbf{Q}_p)$.

We describe the de Rham complex of the étale coverings of Drinfeld’s $p$-adic upper half-plane for ${\rm GL}_2(\mathbf{Q}_p)$. Conjectured by Breuil and Strauch, this description gives a geometric realization of the $p$-adic local Langlands correspondence for certain two-dimensional de Rham representations of ${\rm Gal}(\overline{\mathbf{Q}_p}/\mathbf{Q}_p)$.

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[Ber] $Go to document$ L. Berger, "Représentations $p$-adiques et équations différentielles," Invent. Math., vol. 148, iss. 2, pp. 219-284, 2002.

Show bibtex

@ARTICLE{Ber, author = {Berger, Laurent}, title = {Représentations {$p$}-adiques et équations différentielles}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {148}, year = {2002}, number = {2}, pages = {219--284}, issn = {0020-9910}, mrclass = {14F30 (11S20 12H25 14F40 14G20)}, mrnumber = {1906150}, mrreviewer = {Adolfo QuirÂ${}^3$s}, doi = {10.1007/s002220100202}, zblnumber = {1113.14016}, }
[BerAst] L. Berger, "Équations différentielles $p$-adiques et $(\phi,N)$-modules filtrés," in Représentations $p$-adiques de Groupes $p$-adiques. I. Représentations Galoisiennes et $(\phi,\Gamma)$-Modules, Math. Soc. France, Paris, 2008, vol. 319, pp. 13-38.

Show bibtex

@INCOLLECTION{BerAst, author = {Berger, Laurent}, title = {{\'{E}}quations différentielles {$p$}-adiques et {$(\phi,N)$}-modules filtrés}, booktitle = {Représentations $p$-adiques de Groupes $p$-adiques. I. Représentations Galoisiennes et $(\phi,\Gamma)$-Modules}, series = {Astérisque}, publisher = {Math. Soc. France, Paris}, fjournal = {Astérisque}, volume = {319}, year = {2008}, pages = {13--38}, issn = {0303-1179}, isbn = {978-2-85629-256-3}, mrclass = {11F80 (12H25 14F30)}, mrnumber = {2493215}, mrreviewer = {Michael M. Schein}, zblnumber = {1168.11019}, }
[BB] L. Berger and C. Breuil, "Sur quelques représentations potentiellement cristallines de ${ GL}_2(\Bbb Q_p)$," in Représentations $p$-adiques de Groupes $p$-adiques. I. Représentations Galoisiennes et $(\phi,\Gamma)$-Modules, Math. Soc. France, Paris, 2010, vol. 330, pp. 155-211.

Show bibtex

@INCOLLECTION{BB, author = {Berger, Laurent and Breuil, Christophe}, title = {Sur quelques représentations potentiellement cristallines de {${\rm GL}_2(\bold Q_p)$}}, booktitle = {Représentations $p$-adiques de Groupes $p$-adiques. I. Représentations Galoisiennes et $(\phi,\Gamma)$-Modules}, series = {Astérisque}, publisher = {Math. Soc. France, Paris}, volume = {330}, year = {2010}, pages = {155--211}, issn = {0303-1179}, isbn = {978-2-85629-281-5}, mrclass = {11F70 (11S37 22E50)}, mrnumber = {2642406}, zblnumber = {1243.11063}, }
[Boutot-Carayol] J. -F. Boutot and H. Carayol, "Uniformisation $p$-adique des courbes de Shimura: les théorèmes de \vCerednik et de Drinfeld," in Courbes Modulaires et Courbes de Shimura, Math. Soc. France, Paris, 1991, vol. 196-197, p. 7, 45-158 (1992).

Show bibtex

@INCOLLECTION{Boutot-Carayol, author = {Boutot, J.-F. and Carayol, H.}, title = {Uniformisation {$p$}-adique des courbes de {S}himura: les théorèmes de \v{C}erednik et de {D}rinfeld}, booktitle = {Courbes Modulaires et Courbes de Shimura}, venue = {Orsay, 1987/1988}, series = {Astérisque}, fjournal = {Astérisque}, publisher = {Math. Soc. France, Paris}, volume = {196-197}, year = {1991}, pages = {7, 45--158 (1992)}, issn = {0303-1179}, mrclass = {11G18 (14G20 14G35)}, mrnumber = {1141456}, mrreviewer = {Min Ho Lee}, zblnumber = {0781.14010}, }
[BoutotZink] J. -F. Boutot and . T. Zink, The $p$-adic uniformization of Shimura curves, 2000.

Show bibtex

@MISC{BoutotZink, author = {Boutot, J.-F. and Zink, {\relax Th}.}, title = {The $p$-adic uniformization of {S}himura curves}, year = {2000}, note = {preprint}, zblnumber = {}, }
[Br] $Go to document$ C. Breuil, "Invariant $\mathcal L$ et série spéciale $p$-adique," Ann. Sci. École Norm. Sup. (4), vol. 37, iss. 4, pp. 559-610, 2004.

Show bibtex

@ARTICLE{Br, author = {Breuil, Christophe}, title = {Invariant {$\mathcal L$} et série spéciale {$p$}-adique}, journal = {Ann. Sci. École Norm. Sup. (4)}, fjournal = {Annales Scientifiques de l'École Normale Supérieure. Quatrième Série}, volume = {37}, year = {2004}, number = {4}, pages = {559--610}, issn = {0012-9593}, mrclass = {11F85 (11F80 22E50)}, mrnumber = {2097893}, mrreviewer = {David L. Savitt}, doi = {10.1016/j.ansens.2004.02.001}, zblnumber = {1166.11331}, }
[BBourbaki] C. Breuil, "Correspondance de Langlands $p$-adique, compatibilité local-global et applications [d’après Colmez, Emerton, Kisin, $\ldots$]," in Séminaire Bourbaki: Vol. 2010/2011. Exposés 1027–1042, Math. Soc. France, Paris, 2012, vol. 348, p. exp. no. 1031, viii, 119-147.

Show bibtex

@INCOLLECTION{BBourbaki, author = {Breuil, Christophe}, title = {Correspondance de {L}anglands {$p$}-adique, compatibilité local-global et applications [d'après {C}olmez, {E}merton, {K}isin, {$\ldots$}]}, booktitle = {Séminaire Bourbaki: Vol. 2010/2011. Exposés 1027--1042}, series = {Astérisque}, publisher = {Math. Soc. France, Paris}, volume = {348}, year = {2012}, pages = {Exp. No. 1031, viii, 119--147}, issn = {0303-1179}, isbn = {978-2-85629-351-5}, mrclass = {11S37 (11F70 22E50)}, mrnumber = {3050714}, mrreviewer = {Volker J. Heiermann}, zblnumber = {1280.14006}, }
[Breuil-Schneider] $Go to document$ C. Breuil and P. Schneider, "First steps towards $p$-adic Langlands functoriality," J. Reine Angew. Math., vol. 610, pp. 149-180, 2007.

Show bibtex

@ARTICLE{Breuil-Schneider, author = {Breuil, Christophe and Schneider, Peter}, title = {First steps towards {$p$}-adic {L}anglands functoriality}, journal = {J. Reine Angew. Math.}, fjournal = {Journal für die Reine und Angewandte Mathematik. [Crelle's Journal]}, volume = {610}, year = {2007}, pages = {149--180}, issn = {0075-4102}, mrclass = {11S37 (22E50)}, mrnumber = {2359853}, mrreviewer = {Jacques Tilouine}, doi = {10.1515/CRELLE.2007.070}, zblnumber = {1180.11036}, }
[BS] C. Breuil and M. Strauch, Sur quelques représentations $p$-adiques supercuspidales de ${ GL}_2({\Bbb Q}_p)$.

Show bibtex

@MISC{BS, author = {Breuil, Christophe and Strauch, M.}, title = {Sur quelques représentations $p$-adiques supercuspidales de {${\rm GL}_2({\bold Q}_p)$}}, note = {non publié}, zblnumber = {}, }
[Carayol] H. Carayol, "Non-abelian Lubin-Tate theory," in Automorphic Forms, Shimura Varieties, and $L$-Functions, Vol. II, Clozel, L. and Milne, J. S., Eds., Academic Press, Boston, MA, 1990, vol. 11, pp. 15-39.

Show bibtex

@INCOLLECTION{Carayol, author = {Carayol, H.}, title = {Non-abelian {L}ubin-{T}ate theory}, booktitle = {Automorphic Forms, {S}himura Varieties, and {$L$}-Functions, {V}ol. {II}}, VENUE={{A}nn {A}rbor, {MI}, 1988}, editor = {Clozel, L. and Milne, J. S.}, series = {Perspect. Math.}, volume = {11}, pages = {15--39}, publisher = {Academic Press, Boston, MA}, year = {1990}, mrclass = {11S37 (11F70 11G25 11S31)}, mrnumber = {1044827}, mrreviewer = {Glenn Stevens}, zblnumber = {0704.11049}, }
[Carayol2] $Go to document$ H. Carayol, "Formes modulaires et représentations galoisiennes à valeurs dans un anneau local complet," in $p$-Adic Monodromy and the Birch and Swinnerton-Dyer Conjecture, Amer. Math. Soc., Providence, RI, 1994, vol. 165, pp. 213-237.

Show bibtex

@INCOLLECTION{Carayol2, author = {Carayol, Henri}, title = {Formes modulaires et représentations galoisiennes à valeurs dans un anneau local complet}, booktitle = {{$p$}-Adic Monodromy and the {B}irch and {S}winnerton-{D}yer Conjecture}, VENUE={{B}oston, {MA}, 1991}, series = {Contemp. Math.}, volume = {165}, pages = {213--237}, publisher = {Amer. Math. Soc., Providence, RI}, year = {1994}, mrclass = {11G18 (11F75 11F80)}, mrnumber = {1279611}, mrreviewer = {Douglas L. Ulmer}, doi = {10.1090/conm/165/01601}, zblnumber = {0812.11036}, }
[Chiar] $Go to document$ B. Chiarellotto, "Duality in rigid analysis," in $p$-adic Analysis (Trento, 1989), Springer, Berlin, 1990, vol. 1454, pp. 142-172.

Show bibtex

@INCOLLECTION{Chiar, author = {Chiarellotto, Bruno}, title = {Duality in rigid analysis}, booktitle = {{$p$}-adic {A}nalysis ({T}rento, 1989)}, series = {Lecture Notes in Math.}, volume = {1454}, pages = {142--172}, publisher = {Springer, Berlin}, year = {1990}, mrclass = {32C37 (32E10 32P05)}, mrnumber = {1094850}, mrreviewer = {Peter Ullrich}, doi = {10.1007/BFb0091137}, zblnumber = {0737.32012}, }
[CCsurconv] $Go to document$ F. Cherbonnier and P. Colmez, "Représentations $p$-adiques surconvergentes," Invent. Math., vol. 133, iss. 3, pp. 581-611, 1998.

Show bibtex

@ARTICLE{CCsurconv, author = {Cherbonnier, F. and Colmez, P.}, title = {Représentations {$p$}-adiques surconvergentes}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {133}, year = {1998}, number = {3}, pages = {581--611}, issn = {0020-9910}, mrclass = {11S15 (11S25)}, mrnumber = {1645070}, mrreviewer = {Jean-Pierre Wintenberger}, doi = {10.1007/s002220050255}, zblnumber = {0928.11051}, }
[Cbigone] P. Colmez, "Représentations de ${ GL}_2(\Bbb Q_p)$ et $(\phi,\Gamma)$-modules," Astérisque, iss. 330, pp. 281-509, 2010.

Show bibtex

@ARTICLE{Cbigone, author = {Colmez, Pierre}, title = {Représentations de {${\rm GL}_2(\bold Q_p)$} et {$(\phi,\Gamma)$}-modules}, journal = {Astérisque}, fjournal = {Astérisque}, number = {330}, year = {2010}, pages = {281--509}, issn = {0303-1179}, isbn = {978-2-85629-281-5}, mrclass = {11S37 (11F80)}, mrnumber = {2642409}, mrreviewer = {Fabrizio Andreatta}, zblnumber = {1218.11107}, }
[Ctriang] P. Colmez, "Représentations triangulines de dimension 2," in Représentations $p$-Adiques de groupes $p$-Adiques. I. Représentations Galoisiennes et $(\phi,\Gamma)$-Modules, Math. Soc. France, Paris, 2008, vol. 319, pp. 213-258.

Show bibtex

@INCOLLECTION{Ctriang, mrkey = {2493219}, author = {Colmez, Pierre}, title = {Représentations triangulines de dimension 2}, booktitle = {Représentations $p$-Adiques de groupes $p$-Adiques. I. Représentations Galoisiennes et $(\phi,\Gamma)$-Modules}, series = {Astérisque}, publisher = {Math. Soc. France, Paris}, fjournal = {Astérisque}, volume = {319}, year = {2008}, pages = {213--258}, issn = {0303-1179}, isbn = {978-2-85629-256-3}, mrclass = {11S37 (11S23)}, mrnumber = {2493219}, mrreviewer = {Jan NekovÂ!`\AA �}, zblnumber = {1168.11022}, }
[Cvectan] P. Colmez, "La série principale unitaire de ${ GL}_2(\Bbb Q_p)$," in Représentations $p$-adiques de Groupes $p$-adiques. I. Représentations Galoisiennes et $(\phi,\Gamma)$-Modules, Math. Soc. France, Paris, 2010, vol. 330, pp. 213-262.

Show bibtex

@INCOLLECTION{Cvectan, author = {Colmez, Pierre}, title = {La série principale unitaire de {${\rm GL}_2(\bold Q_p)$}}, booktitle = {Représentations $p$-adiques de Groupes $p$-adiques. I. Représentations Galoisiennes et $(\phi,\Gamma)$-Modules}, series = {Astérisque}, publisher = {Math. Soc. France, Paris}, volume = {330}, year = {2010}, pages = {213--262}, issn = {0303-1179}, isbn = {978-2-85629-281-5}, mrclass = {22E50 (11F80 11F85 11S37)}, mrnumber = {2642407}, mrreviewer = {Laurent N. Berger}, zblnumber = {1242.11095}, }
[Colmezpoids] P. Colmez, Correspondance de Langlands locale $p$-adique et changement de poids.

Show bibtex

@MISC{Colmezpoids, author = {Colmez, Pierre}, title = {Correspondance de {L}anglands locale $p$-adique et changement de poids}, note = {\emph{J.E.M.S.}, à para\^ıtre}, zblnumber = {}, }
[CF] $Go to document$ P. Colmez and J. Fontaine, "Construction des représentations $p$-adiques semi-stables," Invent. Math., vol. 140, iss. 1, pp. 1-43, 2000.

Show bibtex

@ARTICLE{CF, author = {Colmez, Pierre and Fontaine, Jean-Marc}, title = {Construction des représentations {$p$}-adiques semi-stables}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {140}, year = {2000}, number = {1}, pages = {1--43}, issn = {0020-9910}, mrclass = {11S23 (14F30 14F40)}, mrnumber = {1779803}, mrreviewer = {Mark Kisin}, doi = {10.1007/s002220000042}, zblnumber = {1010.14004}, }
[PCD] $Go to document$ P. Colmez, G. Dospinescu, and V. Pavsk=unas, "The $p$-adic local Langlands correspondence for ${ GL}_2(\Bbb Q_p)$," Camb. J. Math., vol. 2, iss. 1, pp. 1-47, 2014.

Show bibtex

@ARTICLE{PCD, author = {Colmez, Pierre and Dospinescu, Gabriel and Paškūnas, Vytautas}, title = {The {$p$}-adic local {L}anglands correspondence for {${\rm GL}_2(\Bbb Q_p)$}}, journal = {Camb. J. Math.}, fjournal = {Cambridge Journal of Mathematics}, volume = {2}, year = {2014}, number = {1}, pages = {1--47}, issn = {2168-0930}, mrclass = {11S37 (11F80 22E50)}, mrnumber = {3272011}, mrreviewer = {Wen-Wei Li}, doi = {10.4310/CJM.2014.v2.n1.a1}, zblnumber = {1312.11090}, }
[CD] $Go to document$ P. Colmez and G. Dospinescu, "Complétés universels de représentations de $\text{GL}_2(\Bbb{Q}_p)$," Algebra Number Theory, vol. 8, iss. 6, pp. 1447-1519, 2014.

Show bibtex

@ARTICLE{CD, mrkey = {3267142}, author = {Colmez, Pierre and Dospinescu, Gabriel}, title = {Complétés universels de représentations de {$\text{GL}_2(\Bbb{Q}_p)$}}, journal = {Algebra Number Theory}, fjournal = {Algebra \& Number Theory}, volume = {8}, year = {2014}, number = {6}, pages = {1447--1519}, issn = {1937-0652}, mrclass = {22E50 (11S37 20G05)}, mrnumber = {3267142}, mrreviewer = {Thá$\gg$�ng Nguyá$\gg$�n-Quang-Ä�á$\gg$�}, doi = {10.2140/ant.2014.8.1447}, zblnumber = {1309.11082}, }
[CDN] P. Colmez, G. Dospinescu, and W. Nizioł, Cohomologie $p$-adique de la tour de Drinfeld: le cas de la dimension $1$.

Show bibtex

@MISC{CDN, author = {Colmez, Pierre and Dospinescu, Gabriel and Nizio{\l}, W.}, title = {Cohomologie $p$-adique de la tour de {D}rinfeld: le cas de la dimension $1$}, note = {en préparation}, arxiv = {1704.08928}, }
[Dat] $Go to document$ J. F. Dat, "Espaces symétriques de Drinfeld et correspondance de Langlands locale," Ann. Sci. École Norm. Sup. (4), vol. 39, iss. 1, pp. 1-74, 2006.

Show bibtex

@ARTICLE{Dat, author = {Dat, Jean François}, title = {Espaces symétriques de {D}rinfeld et correspondance de {L}anglands locale}, journal = {Ann. Sci. École Norm. Sup. (4)}, fjournal = {Annales Scientifiques de l'École Normale Supérieure. Quatrième Série}, volume = {39}, year = {2006}, number = {1}, pages = {1--74}, issn = {0012-9593}, mrclass = {22E50 (11F70 11S37)}, mrnumber = {2224658}, mrreviewer = {Volker J. Heiermann}, doi = {10.1016/j.ansens.2005.11.002}, zblnumber = {1141.22004}, }
[nulles] G. Dospinescu and A. C. Le Bras, Fonctions sur la tour de Drinfeld et la courbe de Fargues-Fontaine.

Show bibtex

@MISC{nulles, author = {Dospinescu, Gabriel and Le Bras, A. C.}, title = {Fonctions sur la tour de {D}rinfeld et la courbe de {F}argues-{F}ontaine}, note = {en préparation}, zblnumber = {}, }
[Annalen] $Go to document$ G. Dospinescu, "Actions infinitésimales dans la correspondance de Langlands locale $p$-adique," Math. Ann., vol. 354, iss. 2, pp. 627-657, 2012.

Show bibtex

@ARTICLE{Annalen, author = {Dospinescu, Gabriel}, title = {Actions infinitésimales dans la correspondance de {L}anglands locale {$p$}-adique}, journal = {Math. Ann.}, fjournal = {Mathematische Annalen}, volume = {354}, year = {2012}, number = {2}, pages = {627--657}, issn = {0025-5831}, mrclass = {22E57}, mrnumber = {2965255}, mrreviewer = {Volker J. Heiermann}, doi = {10.1007/s00208-011-0736-2}, url = {http://dx.doi.org/10.1007/s00208-011-0736-2}, zblnumber = {1259.11110}, }
[DComp] $Go to document$ G. Dospinescu, "Extensions de représentations de de Rham et vecteurs localement algébriques," Compos. Math., vol. 151, iss. 8, pp. 1462-1498, 2015.

Show bibtex

@ARTICLE{DComp, author = {Dospinescu, Gabriel}, title = {Extensions de représentations de de {R}ham et vecteurs localement algébriques}, journal = {Compos. Math.}, fjournal = {Compositio Mathematica}, volume = {151}, year = {2015}, number = {8}, pages = {1462--1498}, issn = {0010-437X}, mrclass = {11F85 (11S85 14G20 22E50)}, mrnumber = {3383164}, mrreviewer = {Sarah Livia Zerbes}, doi = {10.1112/S0010437X14007921}, url = {http://dx.doi.org/10.1112/S0010437X14007921}, zblnumber = {1341.11025}, }
[DJacquet] $Go to document$ G. Dospinescu, "Equations différentielles $p$-adiques et modules de Jacquet analytiques," in Automorphic Forms and Galois Representations. Vol. 1, Cambridge: Cambridge Univ. Press, 2014, vol. 414, pp. 359-374.

Show bibtex

@incollection{DJacquet, author = {Dospinescu, Gabriel}, TITLE = {Equations différentielles {$p$}-adiques et modules de {J}acquet analytiques}, BOOKTITLE = {Automorphic Forms and {G}alois Representations. {V}ol. 1}, SERIES = {London Math. Soc. Lecture Note Ser.}, VOLUME = {414}, PAGES = {359--374}, PUBLISHER = {Cambridge Univ. Press}, ADDRESS = {Cambridge}, YEAR = {2014}, MRCLASS = {11F70 (11S23 11S80 22E50)}, MRNUMBER = {3444229}, ZBLNUMBER = {06589916}, DOI = {10.1017/CBO9781107446335}, }
[Dthese] $Go to document$ G. Dospinescu, Actions infinitésimales dans la correspondance de Langlands locale $p$-adique.

Show bibtex

@misc{Dthese, author = {Dospinescu, Gabriel}, title = {Actions infinitésimales dans la correspondance de {L}anglands locale {$p$}-adique}, note = {thèse de l'Ecole Polytechnique, juin 2012}, url = {https://tel.archives-ouvertes.fr/pastel-00725370/document}, sortyear={2012}, }
[Drinfeld] V. G. Drinfeld, "Coverings of $p$-adic symmetric domains," Funkcional. Anal. i Priložen., vol. 10, iss. 2, pp. 29-40, 1976.

Show bibtex

@ARTICLE{Drinfeld, author = {Drinfeld, V. G.}, title = {Coverings of {$p$}-adic symmetric domains}, journal = {Funkcional. Anal. i Priložen.}, fjournal = {Akademija Nauk SSSR. Funkcional$\prime$nyi Analiz i ego Priloženija}, volume = {10}, year = {1976}, number = {2}, pages = {29--40}, issn = {0374-1990}, mrclass = {14L05 (10D05 14G20 12B25)}, mrnumber = {0422290}, mrreviewer = {Michiel Hazewinkel}, zblnumber = {0346.14010}, }
[Emcomp] M. Emerton, Local-global compatibility in the $p$-adic Langlands programme for ${ GL}_2/\mathbf{Q}$.

Show bibtex

@MISC{Emcomp, author = {Emerton, M.}, title = {Local-global compatibility in the $p$-adic {L}anglands programme for {${\rm GL}_2/\mathbf{Q}$}}, note = {preprint}, zblnumber = {}, }
[faltings] $Go to document$ G. Faltings, "A relation between two moduli spaces studied by V. G. Drinfeld," in Algebraic Number Theory and Algebraic Geometry, Amer. Math. Soc., Providence, RI, 2002, vol. 300, pp. 115-129.

Show bibtex

@INCOLLECTION{faltings, author = {Faltings, Gerd}, title = {A relation between two moduli spaces studied by {V}. {G}. {D}rinfeld}, booktitle = {Algebraic {N}umber {T}heory and {A}lgebraic {G}eometry}, series = {Contemp. Math.}, volume = {300}, pages = {115--129}, publisher = {Amer. Math. Soc., Providence, RI}, year = {2002}, mrclass = {14L05 (14G22)}, mrnumber = {1936369}, mrreviewer = {Noriko Yui}, doi = {10.1090/conm/300/05145}, url = {http://dx.doi.org/10.1090/conm/300/05145}, zblnumber = {1062.14059}, }
[FGL] L. Fargues, A. Genestier, and V. Lafforgue, L’isomorphisme Entre les Tours de Lubin-Tate et de Drinfeld, Birkhäuser Verlag, Basel, 2008, vol. 262.

Show bibtex

@BOOK{FGL, author = {Fargues, Laurent and Genestier, Alain and Lafforgue, Vincent}, title = {L'isomorphisme Entre les Tours de {L}ubin-{T}ate et de {D}rinfeld}, series = {Progr. in Math.}, volume = {262}, publisher = {Birkhäuser Verlag, Basel}, year = {2008}, pages = {xxii+406}, isbn = {978-3-7643-8455-5}, mrclass = {14L05 (11R39 14-06 14G22 14G35)}, mrnumber = {2441311}, mrreviewer = {Eva Viehmann}, zblnumber = {1136.14001}, }
[Farguesthese] L. Fargues, "Cohomologie des espaces de modules de groupes $p$-divisibles et correspondances de Langlands locales," in Variétés de Shimura, Espaces de Rapoport-Zink et Correspondances de Langlands Locales, Math. Soc. France, Paris, 2004, vol. 291, pp. 1-199.

Show bibtex

@INCOLLECTION{Farguesthese, author = {Fargues, Laurent}, title = {Cohomologie des espaces de modules de groupes {$p$}-divisibles et correspondances de {L}anglands locales}, booktitle = {Variétés de Shimura, Espaces de Rapoport-Zink et Correspondances de Langlands Locales}, series = {Astérisque}, volume = {291}, publisher = {Math. Soc. France, Paris}, year = {2004}, pages = {1--199}, issn = {0303-1179}, mrclass = {11G18 (11S37 14G32 14G35 14L05)}, mrnumber = {2074714}, mrreviewer = {James Milne}, zblnumber = {1196.11087}, }
[FoGrot] J. Fontaine, "Représentations $p$-adiques des corps locaux. I," in The Grothendieck Festschrift, Vol. II, Birkhäuser Boston, Boston, MA, 1990, vol. 87, pp. 249-309.

Show bibtex

@INCOLLECTION{FoGrot, author = {Fontaine, Jean-Marc}, title = {Représentations {$p$}-adiques des corps locaux. {I}}, booktitle = {The {G}rothendieck {F}estschrift, {V}ol. {II}}, series = {Progr. Math.}, volume = {87}, pages = {249--309}, publisher = {Birkhäuser Boston, Boston, MA}, year = {1990}, mrclass = {11S23 (14F30 14L05)}, mrnumber = {1106901}, mrreviewer = {Rutger Noot}, zblnumber = {0743.11066}, }
[peradiques] J. Fontaine, "Représentations $l$-adiques potentiellement semi-stables," in Périodes $p$-Adiques, Math. Soc. France, Paris, 1994, vol. 223, pp. 321-347.

Show bibtex

@INCOLLECTION{peradiques, author = {Fontaine, Jean-Marc}, title = {Représentations {$l$}-adiques potentiellement semi-stables}, booktitle = {Périodes $p$-Adiques}, venue = {Bures-sur-Yvette, 1988}, series = {Astérisque}, fjournal = {Astérisque}, publisher = {Math. Soc. France, Paris}, volume = {223}, year = {1994}, pages = {321--347}, issn = {0303-1179}, mrclass = {14F20 (11G25 14F30 14G20)}, mrnumber = {1293977}, mrreviewer = {Adolfo QuirÂ${}^3$s}, zblnumber = {0873.14020}, }
[FonAst] J. Fontaine, "Arithmétique des représentations galoisiennes $p$-adiques," in Cohomologies $p$-adiques et Applications Arithmétiques. III, Math. Soc. France, Paris, 2004, vol. 295, p. xi, 1-115.

Show bibtex

@INCOLLECTION{FonAst, author = {Fontaine, Jean-Marc}, title = {Arithmétique des représentations galoisiennes {$p$}-adiques}, booktitle = {Cohomologies $p$-adiques et Applications Arithmétiques. III}, series = {Astérisque}, volume = {295}, year = {2004}, publisher = {Math. Soc. France, Paris}, pages = {xi, 1--115}, issn = {0303-1179}, mrclass = {11F80 (11F85 11S15 11S20 11S25 13K05 14F30)}, mrnumber = {2104360}, mrreviewer = {Laurent N. Berger}, zblnumber = {1142.11335}, }
[Frommer] H. Frommer, The locally analytic principal series of split reductive groups, 2003.

Show bibtex

@MISC{Frommer, author = {Frommer, H.}, title = {The locally analytic principal series of split reductive groups}, note = {preprint}, year = {2003}, zblnumber = {}, }
[GH] $Go to document$ M. J. Hopkins and B. H. Gross, "Equivariant vector bundles on the Lubin-Tate moduli space," in Topology and representation theory (Evanston, IL, 1992), Amer. Math. Soc., Providence, RI, 1994, vol. 158, pp. 23-88.

Show bibtex

@INCOLLECTION{GH, author = {Hopkins, M. J. and Gross, B. H.}, title = {Equivariant vector bundles on the {L}ubin-{T}ate moduli space}, booktitle = {Topology and representation theory ({E}vanston, {IL}, 1992)}, series = {Contemp. Math.}, volume = {158}, pages = {23--88}, publisher = {Amer. Math. Soc., Providence, RI}, year = {1994}, mrclass = {14L05 (11S31 12H25 55R91)}, mrnumber = {1263712}, mrreviewer = {Burt Totaro}, doi = {10.1090/conm/158/01453}, url = {http://dx.doi.org/10.1090/conm/158/01453}, zblnumber = {0807.14037}, }
[GK1] $Go to document$ E. Grosse-Klönne, "De Rham cohomology of rigid spaces," Math. Z., vol. 247, iss. 2, pp. 223-240, 2004.

Show bibtex

@ARTICLE{GK1, author = {Grosse-Klönne, Elmar}, title = {De {R}ham cohomology of rigid spaces}, journal = {Math. Z.}, fjournal = {Mathematische Zeitschrift}, volume = {247}, year = {2004}, number = {2}, pages = {223--240}, issn = {0025-5874}, mrclass = {14F40 (14G22)}, mrnumber = {2064051}, mrreviewer = {Martin C. Olsson}, doi = {10.1007/s00209-003-0544-9}, url = {http://dx.doi.org/10.1007/s00209-003-0544-9}, zblnumber = {1078.14026}, }
[GK2] $Go to document$ E. Grosse-Klönne, "Rigid analytic spaces with overconvergent structure sheaf," J. Reine Angew. Math., vol. 519, pp. 73-95, 2000.

Show bibtex

@ARTICLE{GK2, author = {Grosse-Klönne, Elmar}, title = {Rigid analytic spaces with overconvergent structure sheaf}, journal = {J. Reine Angew. Math.}, fjournal = {Journal für die Reine und Angewandte Mathematik. [Crelle's Journal]}, volume = {519}, year = {2000}, pages = {73--95}, issn = {0075-4102}, mrclass = {14G22 (14F40)}, mrnumber = {1739729}, mrreviewer = {Mark Kisin}, doi = {10.1515/crll.2000.018}, url = {http://dx.doi.org/10.1515/crll.2000.018}, zblnumber = {0945.14013}, }
[GKrig] $Go to document$ E. Grosse-Klönne, "Frobenius and monodromy operators in rigid analysis, and Drinfel$\prime$d’s symmetric space," J. Algebraic Geom., vol. 14, iss. 3, pp. 391-437, 2005.

Show bibtex

@ARTICLE{GKrig, author = {Grosse-Klönne, Elmar}, title = {Frobenius and monodromy operators in rigid analysis, and {D}rinfel$\prime$d's symmetric space}, journal = {J. Algebraic Geom.}, fjournal = {Journal of Algebraic Geometry}, volume = {14}, year = {2005}, number = {3}, pages = {391--437}, issn = {1056-3911}, mrclass = {14G22 (14F30 14F40)}, mrnumber = {2129006}, mrreviewer = {Alessandra Bertapelle}, doi = {10.1090/S1056-3911-05-00402-9}, url = {http://dx.doi.org/10.1090/S1056-3911-05-00402-9}, zblnumber = {1084.14021}, }
[HarrisInv] $Go to document$ M. Harris, "Supercuspidal representations in the cohomology of Drinfeld’s upper half spaces; elaboration of Carayol’s program," Invent. Math., vol. 129, iss. 1, pp. 75-119, 1997.

Show bibtex

@ARTICLE{HarrisInv, author = {Harris, Michael}, title = {Supercuspidal representations in the cohomology of {D}rinfeld's upper half spaces; elaboration of {C}arayol's program}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {129}, year = {1997}, number = {1}, pages = {75--119}, issn = {0020-9910}, mrclass = {11S37 (11F70 11F72 11G18 22E50 22E55)}, mrnumber = {1464867}, mrreviewer = {Ernst-Wilhelm Zink}, doi = {10.1007/s002220050159}, url = {http://dx.doi.org/10.1007/s002220050159}, zblnumber = {0886.11029}, }
[HT] M. Harris and R. Taylor, The Geometry and Cohomology of Some Simple Shimura Varieties, Princeton University Press, Princeton, NJ, 2001, vol. 151.

Show bibtex

@BOOK{HT, author = {Harris, Michael and Taylor, Richard}, title = {The Geometry and Cohomology of Some Simple {S}himura Varieties}, series = {Ann. of Math. Stud.}, volume = {151}, note = {with an appendix by Vladimir G. Berkovich}, publisher = {Princeton University Press, Princeton, NJ}, year = {2001}, pages = {viii+276}, isbn = {0-691-09090-4}, mrclass = {11G18 (11F70 11S37 14G35 22E45)}, mrnumber = {1876802}, mrreviewer = {James Milne}, zblnumber = {1036.11027}, }
[henniart] $Go to document$ G. Henniart, "Sur l’unicité des types pour ${{ GL}}_2$, appendice à “Multiplicités modulaires et représentations de ${ GL}_2({\bf Z}_p)$ et de ${ Gal}(\overline{\bf Q}_p/{\bf Q}_p)$ en $l=p$” par C. Breuil et A. Mézard," Duke Math. J., vol. 115, iss. 2, pp. 205-310, 2002.

Show bibtex

@ARTICLE{henniart, author = {Henniart, G.}, title = {Sur l'unicité des types pour ${{\rm GL}}_2$, appendice à ``{M}ultiplicités modulaires et représentations de {${\rm GL}_2({\bf Z}_p)$} et de {${\rm Gal}(\overline{\bf Q}_p/{\bf Q}_p)$} en {$l=p$}'' par {C. B}reuil et {A. M}ézard}, journal = {Duke Math. J.}, volume = {115}, number = {2}, year = {2002}, pages = { 205--310}, issn = {0012-7094}, mrclass = {11F80 (11F85 11S23)}, mrnumber = {1944572}, mrreviewer = {Jacques Tilouine}, doi = {10.1215/S0012-7094-02-11522-1}, zblnumber = {}, }
[KPL] $Go to document$ K. S. Kedlaya, J. Pottharst, and L. Xiao, "Cohomology of arithmetic families of $(\varphi,\Gamma)$-modules," J. Amer. Math. Soc., vol. 27, iss. 4, pp. 1043-1115, 2014.

Show bibtex

@ARTICLE{KPL, mrkey = {3230818}, author = {Kedlaya, Kiran S. and Pottharst, Jonathan and Xiao, Liang}, title = {Cohomology of arithmetic families of {$(\varphi,\Gamma)$}-modules}, journal = {J. Amer. Math. Soc.}, fjournal = {Journal of the American Mathematical Society}, volume = {27}, year = {2014}, number = {4}, pages = {1043--1115}, issn = {0894-0347}, mrclass = {11F33 (11R23 11S25 11S31 13D09)}, mrnumber = {3230818}, doi = {10.1090/S0894-0347-2014-00794-3}, zblnumber = {1314.11028}, }
[Kedbook] $Go to document$ K. S. Kedlaya, $p$-adic Differential Equations, Cambridge University Press, Cambridge, 2010, vol. 125.

Show bibtex

@BOOK{Kedbook, author = {Kedlaya, Kiran S.}, title = {{$p$}-adic Differential Equations}, series = {Cambridge Stud. Adv. Math.}, volume = {125}, publisher = {Cambridge University Press, Cambridge}, year = {2010}, pages = {xviii+380}, isbn = {978-0-521-76879-5}, mrclass = {12H25 (14G22)}, mrnumber = {2663480}, mrreviewer = {Nobuo Tsuzuki}, doi = {10.1017/CBO9780511750922}, url = {http://dx.doi.org/10.1017/CBO9780511750922}, zblnumber = {1213.12009}, }
[Kiehl] $Go to document$ R. Kiehl, "Theorem A und Theorem B in der nichtarchimedischen Funktionentheorie," Invent. Math., vol. 2, pp. 256-273, 1967.

Show bibtex

@ARTICLE{Kiehl, author = {Kiehl, Reinhardt}, title = {Theorem {A} und {T}heorem {B} in der nichtarchimedischen {F}unktionentheorie}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {2}, year = {1967}, pages = {256--273}, issn = {0020-9910}, mrclass = {32.50 (32.20)}, mrnumber = {0210949}, mrreviewer = {A. F. Monna}, doi = {10.1007/BF01425404}, url = {http://dx.doi.org/10.1007/BF01425404}, zblnumber = {0202.20201}, }
[kisin] M. Kisin, "Deformations of $G_{\Bbb Q_p}$ and ${ GL}_2(\Bbb Q_p)$ representations," Astérisque, iss. 330, pp. 511-528, 2010.

Show bibtex

@ARTICLE{kisin, author = {Kisin, Mark}, title = {Deformations of {$G_{\Bbb Q_p}$} and {${\rm GL}_2(\Bbb Q_p)$} representations}, journal = {Astérisque}, fjournal = {Astérisque}, number = {330}, year = {2010}, pages = {511--528}, issn = {0303-1179}, isbn = {978-2-85629-281-5}, mrclass = {11S37 (11S20)}, mrnumber = {2642410}, mrreviewer = {Jerzy Browkin}, zblnumber = {1233.11126}, }
[Kohl] $Go to document$ J. Kohlhaase, "Lubin-Tate and Drinfeld bundles," Tohoku Math. J. (2), vol. 63, iss. 2, pp. 217-254, 2011.

Show bibtex

@ARTICLE{Kohl, author = {Kohlhaase, Jan}, title = {Lubin-{T}ate and {D}rinfeld bundles}, journal = {Tohoku Math. J. (2)}, fjournal = {The Tohoku Mathematical Journal. Second Series}, volume = {63}, year = {2011}, number = {2}, pages = {217--254}, issn = {0040-8735}, mrclass = {11G18 (11F80 14G35)}, mrnumber = {2812452}, mrreviewer = {Mihran Papikian}, doi = {10.2748/tmj/1309952087}, url = {http://dx.doi.org/10.2748/tmj/1309952087}, zblnumber = {1287.11076}, }
[LXZ] $Go to document$ R. Liu, B. Xie, and Y. Zhang, "Locally analytic vectors of unitary principal series of ${ GL}_2(\Bbb Q_p)$," Ann. Sci. Éc. Norm. Supér. (4), vol. 45, iss. 1, pp. 167-190, 2012.

Show bibtex

@ARTICLE{LXZ, author = {Liu, Ruochuan and Xie, Bingyong and Zhang, Yuancao}, title = {Locally analytic vectors of unitary principal series of {${\rm GL}_2(\Bbb Q_p)$}}, journal = {Ann. Sci. Éc. Norm. Supér. (4)}, fjournal = {Annales Scientifiques de l'École Normale Supérieure. Quatrième Série}, volume = {45}, year = {2012}, number = {1}, pages = {167--190}, issn = {0012-9593}, mrclass = {11S37 (22E50)}, mrnumber = {2961790}, mrreviewer = {Dubravka Ban}, zblnumber = {1320.11112}, URL = {http://smf4.emath.fr/Publications/AnnalesENS/4_45/html/ens_ann-sc_45_167-190.php}, }
[LT] $Go to document$ J. Lubin and J. Tate, "Formal moduli for one-parameter formal Lie groups," Bull. Soc. Math. France, vol. 94, pp. 49-59, 1966.

Show bibtex

@ARTICLE{LT, author = {Lubin, Jonathan and Tate, John}, title = {Formal moduli for one-parameter formal {L}ie groups}, journal = {Bull. Soc. Math. France}, fjournal = {Bulletin de la Société Mathématique de France}, volume = {94}, year = {1966}, pages = {49--59}, issn = {0037-9484}, mrclass = {14.50}, mrnumber = {0238854}, mrreviewer = {J. DieudonnÂ\copyright{}}, url = {http://archive.numdam.org/article/BSMF_1966__94__49_0.pdf}, zblnumber = {0156.04105}, }
[Marmora] A. Marmora, "Irrégularité et conducteur de Swan $p$-adiques," Doc. Math., vol. 9, pp. 413-433, 2004.

Show bibtex

@ARTICLE{Marmora, author = {Marmora, Adriano}, title = {Irrégularité et conducteur de {S}wan {$p$}-adiques}, journal = {Doc. Math.}, fjournal = {Documenta Mathematica}, volume = {9}, year = {2004}, pages = {413--433}, issn = {1431-0635}, mrclass = {11S15 (11F80 11F85 12H25)}, mrnumber = {2117421}, mrreviewer = {Laurent N. Berger}, zblnumber = {1071.11065}, }
[Morita1] $Go to document$ Y. Morita, "A $p$-adic theory of hyperfunctions. I," Publ. Res. Inst. Math. Sci., vol. 17, iss. 1, pp. 1-24, 1981.

Show bibtex

@ARTICLE{Morita1, author = {Morita, Yasuo}, title = {A {$p$}-adic theory of hyperfunctions. {I}}, journal = {Publ. Res. Inst. Math. Sci.}, fjournal = {Kyoto University. Research Institute for Mathematical Sciences. Publications}, volume = {17}, year = {1981}, number = {1}, pages = {1--24}, issn = {0034-5318}, mrclass = {12B40 (12B30)}, mrnumber = {0613933}, mrreviewer = {G. Christol}, doi = {10.2977/prims/1195186702}, url = {http://dx.doi.org/10.2977/prims/1195186702}, zblnumber = {0457.12010}, }
[luepan] $Go to document$ L. Pan, "First covering of the Drinfel’d upper half-plane and Banach representations of ${ GL}_2(\mathbb{Q}_p)$," Algebra Number Theory, vol. 11, pp. 405-503, 2017.

Show bibtex

@ARTICLE{luepan, author = {Pan, Lue}, title = {First covering of the {D}rinfel'd upper half-plane and {B}anach representations of {${\rm GL}_2(\mathbb{Q}_p)$}}, journal = {Algebra Number Theory}, fjournal = {Algebra and Number Theory}, year = {2017}, volume = {11}, pages = {405--503}, zblnumber = {}, DOI = {10.2140/ant.2017.11.405}, mrnumber={3641878}, }
[Orlik] S. Orlik, "The de Rham cohomology of Drinfeld’s half space," Münster J. Math., vol. 8, iss. 1, pp. 169-179, 2015.

Show bibtex

@ARTICLE{Orlik, author = {Orlik, Sascha}, title = {The de {R}ham cohomology of {D}rinfeld's half space}, journal = {Münster J. Math.}, fjournal = {Münster Journal of Mathematics}, volume = {8}, year = {2015}, number = {1}, pages = {169--179}, issn = {1867-5778}, mrclass = {11F85 (14F40 14G22)}, mrnumber = {3549524}, mrreviewer = {Francesc Bars}, zblnumber = {1358.11065}, }
[Pa] $Go to document$ V. Pavsk=unas, "The image of Colmez’s Montreal functor," Publ. Math. Inst. Hautes Études Sci., vol. 118, pp. 1-191, 2013.

Show bibtex

@ARTICLE{Pa, mrkey = {3150248}, author = {Paškūnas, Vytautas}, title = {The image of {C}olmez's {M}ontreal functor}, journal = {Publ. Math. Inst. Hautes Études Sci.}, fjournal = {Publications Mathématiques. Institut de Hautes Études Scientifiques}, volume = {118}, year = {2013}, pages = {1--191}, issn = {0073-8301}, mrclass = {22E35 (11S37 22E50)}, mrnumber = {3150248}, mrreviewer = {Ivan MatiÄ�}, doi = {10.1007/s10240-013-0049-y}, zblnumber = {1297.22021}, }
[PSS] $Go to document$ D. Patel, M. Strauch, and T. Schmidt, "Locally analytic representations of ${ GL}(2,L)$ via semistable models of $\mathbb{P}^1$," J. Inst. Math. Jussieu, p. 63, 2017.

Show bibtex

@ARTICLE{PSS, author = {Patel, D. and Strauch, M. and Schmidt, T.}, title = {Locally analytic representations of {${\rm GL}(2,L)$} via semistable models of $\mathbb{P}^1$}, journal = {J. Inst. Math. Jussieu}, fjournal = {Journal de l'Institut mathématique de Jussieu}, year = {2017}, pages = {63 pp.}, doi = {10.1017/S1474748016000396}, zblnumber = {}, }
[RZ] $Go to document$ M. Rapoport and T. Zink, Period spaces for $p$-divisible groups, Princeton University Press, Princeton, NJ, 1996, vol. 141.

Show bibtex

@BOOK{RZ, author = {Rapoport, M. and Zink, Th.}, title = {Period spaces for {$p$}-divisible groups}, series = {Annals of Mathematics Studies}, volume = {141}, publisher = {Princeton University Press, Princeton, NJ}, year = {1996}, pages = {xxii+324}, isbn = {0-691-02782-X; 0-691-02781-1}, mrclass = {14G20 (11G18 14F30 14L05 14M15 20G05 20G25)}, mrnumber = {1393439}, mrreviewer = {Robert E. Kottwitz}, doi = {10.1515/9781400882601}, url = {http://dx.doi.org/10.1515/9781400882601}, zblnumber = {0873.14039}, }
[Saito] $Go to document$ T. Saito, "Modular forms and $p$-adic Hodge theory," Invent. Math., vol. 129, iss. 3, pp. 607-620, 1997.

Show bibtex

@ARTICLE{Saito, author = {Saito, Takeshi}, title = {Modular forms and {$p$}-adic {H}odge theory}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {129}, year = {1997}, number = {3}, pages = {607--620}, issn = {0020-9910}, mrclass = {11F80 (11F33 14F30)}, mrnumber = {1465337}, mrreviewer = {Abdellah Mokrane}, doi = {10.1007/s002220050175}, url = {http://dx.doi.org/10.1007/s002220050175}, zblnumber = {0877.11034}, }
[SS] $Go to document$ P. Schneider and U. Stuhler, "The cohomology of $p$-adic symmetric spaces," Invent. Math., vol. 105, iss. 1, pp. 47-122, 1991.

Show bibtex

@ARTICLE{SS, author = {Schneider, P. and Stuhler, U.}, title = {The cohomology of {$p$}-adic symmetric spaces}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {105}, year = {1991}, number = {1}, pages = {47--122}, issn = {0020-9910}, mrclass = {11F85 (14G20)}, mrnumber = {1109620}, mrreviewer = {Gerd Faltings}, doi = {10.1007/BF01232257}, url = {http://dx.doi.org/10.1007/BF01232257}, zblnumber = {0751.14016}, }
[STMorita] $Go to document$ P. Schneider and J. Teitelbaum, "An integral transform for $p$-adic symmetric spaces," Duke Math. J., vol. 86, iss. 3, pp. 391-433, 1997.

Show bibtex

@ARTICLE{STMorita, author = {Schneider, Peter and Teitelbaum, Jeremy}, title = {An integral transform for {$p$}-adic symmetric spaces}, journal = {Duke Math. J.}, fjournal = {Duke Mathematical Journal}, volume = {86}, year = {1997}, number = {3}, pages = {391--433}, issn = {0012-7094}, mrclass = {11F85 (14F40 22E50)}, mrnumber = {1432303}, mrreviewer = {Andrea Mori}, doi = {10.1215/S0012-7094-97-08612-9}, url = {http://dx.doi.org/10.1215/S0012-7094-97-08612-9}, zblnumber = {0885.14012}, }
[ST] $Go to document$ P. Schneider and J. Teitelbaum, "Locally analytic distributions and $p$-adic representation theory, with applications to ${ GL}_2$," J. Amer. Math. Soc., vol. 15, iss. 2, pp. 443-468, 2002.

Show bibtex

@ARTICLE{ST, author = {Schneider, Peter and Teitelbaum, Jeremy}, title = {Locally analytic distributions and {$p$}-adic representation theory, with applications to {${\rm GL}_2$}}, journal = {J. Amer. Math. Soc.}, fjournal = {Journal of the American Mathematical Society}, volume = {15}, year = {2002}, number = {2}, pages = {443--468}, issn = {0894-0347}, mrclass = {11S80 (22E50)}, mrnumber = {1887640}, mrreviewer = {Volker J. Heiermann}, doi = {10.1090/S0894-0347-01-00377-0}, url = {http://dx.doi.org/10.1090/S0894-0347-01-00377-0}, zblnumber = {1028.11071}, }
[STInv] $Go to document$ P. Schneider and J. Teitelbaum, "Algebras of $p$-adic distributions and admissible representations," Invent. Math., vol. 153, iss. 1, pp. 145-196, 2003.

Show bibtex

@ARTICLE{STInv, mrkey = {1990669}, author = {Schneider, Peter and Teitelbaum, Jeremy}, title = {Algebras of {$p$}-adic distributions and admissible representations}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {153}, year = {2003}, number = {1}, pages = {145--196}, issn = {0020-9910}, mrclass = {22E50}, mrnumber = {1990669}, mrreviewer = {Marko TadiÄ�}, doi = {10.1007/s00222-002-0284-1}, zblnumber = {1028.11070}, }
[boundary] P. Schneider and J. Teitelbaum, "$p$-adic boundary values," Astérisque, vol. 278, pp. 51-125, 2004.

Show bibtex

@ARTICLE{boundary, author = {Schneider, Peter and Teitelbaum, Jeremy}, title = {$p$-adic boundary values}, year = {2004}, journal = {Astérisque}, volume = {278}, pages = {51--125}, mrnumber = {1922824}, zblnumber = {1051.14024}, note={[correction in {\em Astérisque} {\bf 295} (2004), 291--299, \mr{2104362}]}, }
[Schraen] $Go to document$ B. Schraen, "Représentations $p$-adiques de ${ GL}_2(L)$ et catégories dérivées," Israel J. Math., vol. 176, pp. 307-361, 2010.

Show bibtex

@ARTICLE{Schraen, author = {Schraen, Benjamin}, title = {Représentations {$p$}-adiques de {${\rm GL}_2(L)$} et catégories dérivées}, journal = {Israel J. Math.}, fjournal = {Israel Journal of Mathematics}, volume = {176}, year = {2010}, pages = {307--361}, issn = {0021-2172}, mrclass = {22E50 (11F70)}, mrnumber = {2653197}, mrreviewer = {Anne-Marie H. Aubert}, doi = {10.1007/s11856-010-0031-z}, url = {http://dx.doi.org/10.1007/s11856-010-0031-z}, zblnumber = {1210.11066}, }
[Shodge] $Go to document$ P. Scholze, "$p$-adic Hodge theory for rigid-analytic varieties," Forum Math. Pi, vol. 1, iss. e1, p. 77, 2013.

Show bibtex

@ARTICLE{Shodge, author = {Scholze, Peter}, title = {{$p$}-adic {H}odge theory for rigid-analytic varieties}, journal = {Forum Math. Pi}, fjournal = {Forum of Mathematics. Pi}, volume = {1}, year = {2013}, number = {e1}, pages = {77}, issn = {2050-5086}, mrclass = {14G22 (14C30 14F30 14G20 32J27 32P05)}, mrnumber = {3090230}, mrreviewer = {Hui June Zhu}, doi = {10.1017/fmp.2013.1}, url = {http://dx.doi.org/10.1017/fmp.2013.1}, zblnumber = {1297.14023}, }
[Scholze] P. Scholze, On the $p$-adic cohomology of the Lubin-Tate tower.

Show bibtex

@MISC{Scholze, author = {Scholze, Peter}, title = {On the $p$-adic cohomology of the {L}ubin-{T}ate tower}, sortyear = {2017}, note = {preprint}, arxiv = {1506.04022}, }
[Shalit] $Go to document$ E. De Shalit, "Residues on buildings and de Rham cohomology of $p$-adic symmetric domains," Duke Math. J., vol. 106, iss. 1, pp. 123-191, 2001.

Show bibtex

@ARTICLE{Shalit, author = {De Shalit, Ehud}, title = {Residues on buildings and de {R}ham cohomology of {$p$}-adic symmetric domains}, journal = {Duke Math. J.}, fjournal = {Duke Mathematical Journal}, volume = {106}, year = {2001}, number = {1}, pages = {123--191}, issn = {0012-7094}, mrclass = {14F40 (20E42 20G25)}, mrnumber = {1810368}, mrreviewer = {Ernst-Wilhelm Zink}, doi = {10.1215/S0012-7094-01-10615-7}, zblnumber = {1103.14010}, }
[Strauchcc] $Go to document$ M. Strauch, "Geometrically connected components of Lubin-Tate deformation spaces with level structures," Pure Appl. Math. Q., vol. 4, iss. 4, special issue in honor of Jean-Pierre Serre. Part 1, pp. 1215-1232, 2008.

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@ARTICLE{Strauchcc, author = {Strauch, Matthias}, title = {Geometrically connected components of {L}ubin-{T}ate deformation spaces with level structures}, journal = {Pure Appl. Math. Q.}, fjournal = {Pure and Applied Mathematics Quarterly}, volume = {4}, year = {2008}, number = {4, special issue in honor of Jean-Pierre Serre. Part 1}, pages = {1215--1232}, issn = {1558-8599}, mrclass = {11G09 (11S31)}, mrnumber = {2441699}, mrreviewer = {Eva Viehmann}, doi = {10.4310/PAMQ.2008.v4.n4.a10}, url = {http://dx.doi.org/10.4310/PAMQ.2008.v4.n4.a10}, zblnumber = {1193.11112}, }
[taylor] R. Taylor, "On the meromorphic continuation of degree two $L$-functions," Doc. Math., iss. Extra Vol., pp. 729-779, 2006.

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@ARTICLE{taylor, author = {Taylor, Richard}, title = {On the meromorphic continuation of degree two {$L$}-functions}, journal = {Doc. Math.}, fjournal = {Documenta Mathematica}, year = {2006}, number = {Extra Vol.}, pages = {729--779}, issn = {1431-0635}, mrclass = {11R39 (11F80 11G40)}, mrnumber = {2290604}, mrreviewer = {M. Ram Murty}, zblnumber = {1138.11051}, }
[teitel] $Go to document$ J. Teitelbaum, "Geometry of an étale covering of the $p$-adic upper half plane," Ann. Inst. Fourier (Grenoble), vol. 40, iss. 1, pp. 68-78, 1990.

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@ARTICLE{teitel, author = {Teitelbaum, Jeremy}, title = {Geometry of an étale covering of the {$p$}-adic upper half plane}, journal = {Ann. Inst. Fourier (Grenoble)}, fjournal = {Université de Grenoble. Annales de l'Institut Fourier}, volume = {40}, year = {1990}, number = {1}, pages = {68--78}, issn = {0373-0956}, mrclass = {11G18 (11F85 11G09 14G20)}, mrnumber = {1056774}, mrreviewer = {Ernst-Ulrich Gekeler}, doi = {10.5802/aif.1203}, zblnumber = {0687.14019}, }

Revêtements du demi-plan de Drinfeld et correspondance de Langlands $p$-adique

Abstract

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