Abstract
We prove the overholonomicity of overconvergent $F$-isocrystals over
smooth varieties. This implies that the notions of overholonomicity and devissability in overconvergent $F$-isocrystals are equivalent. Then the overholonomicity is stable under tensor products. So, the overholonomicity gives a $p$-adic cohomology stable under Grothendieck’s cohomological operations.
-
[AB1] Y. André and F. Baldassarri, De Rham Cohomology of Differential Modules on Algebraic Varieties, Basel: Birkhäuser, 2001, vol. 189.
@book {AB1, MRKEY = {1807281},
AUTHOR = {Andr{é},
Yves and Baldassarri, Francesco},
TITLE = {De {R}ham Cohomology of Differential Modules on Algebraic Varieties},
SERIES = {Progr. Math.},
VOLUME = {189},
PUBLISHER = {Birkhäuser},
ADDRESS = {Basel},
YEAR = {2001},
PAGES = {viii+214},
ISBN = {3-7643-6348-7},
MRCLASS = {14F40 (12H20 14F30 14G22 32C38)},
MRNUMBER = {1807281},
MRREVIEWER = {Adolfo Quir{ó}s},
ZBLNUMBER = {0995.14003},
} -
[BB1] F. Baldassarri and P. Berthelot, "On Dwork cohomology for singular hypersurfaces," in Geometric Aspects of Dwork Theory. Vol. I, II, Walter de Gruyter GmbH & Co. KG, Berlin, 2004, pp. 177-244.
@incollection {BB1, MRKEY = {2023290},
AUTHOR = {Baldassarri, Francesco and Berthelot, Pierre},
TITLE = {On {D}work cohomology for singular hypersurfaces},
BOOKTITLE = {Geometric Aspects of {D}work Theory. {V}ol. {I},
{II}},
PAGES = {177--244},
PUBLISHER = {Walter de Gruyter GmbH \& Co. KG, Berlin},
YEAR = {2004},
MRCLASS = {14F30 (14F40 14G10)},
MRNUMBER = {2023290},
MRREVIEWER = {Jean-Yves {É}tesse},
ZBLNUMBER = {1117.14022},
} -
[BC1]
F. Baldassarri and B. Chiarellotto, "On Christol’s theorem. A generalization to systems of PDEs with logarithmic singularities depending upon parameters," in $p$-Adic Methods in Number Theory and Algebraic Geometry, Providence, RI: Amer. Math. Soc., 1992, vol. 133, pp. 1-24.@incollection {BC1, MRKEY = {1183967},
AUTHOR = {Baldassarri, Francesco and Chiarellotto, Bruno},
TITLE = {On {C}hristol's theorem. {A} generalization to systems of {PDE}s with logarithmic singularities depending upon parameters},
BOOKTITLE = {{$p$}-Adic Methods in Number Theory and Algebraic Geometry},
SERIES = {Contemp. Math.},
VOLUME = {133},
PAGES = {1--24},
PUBLISHER = {Amer. Math. Soc.},
ADDRESS = {Providence, RI},
YEAR = {1992},
MRCLASS = {12H25 (12J27)},
MRNUMBER = {1183967},
MRREVIEWER = {Takashi Harase},
DOI = {10.1090/conm/133/1183967},
ZBLNUMBER = {0768.12006},
} -
[BC2] F. Baldassarri and B. Chiarellotto, "Algebraic versus rigid cohomology with logarithmic coefficients," in Barsotti Symposium in Algebraic Geometry, San Diego, CA: Academic Press, 1994, vol. 15, pp. 11-50.
@incollection {BC2, MRKEY = {1307391},
AUTHOR = {Baldassarri, Francesco and Chiarellotto, Bruno},
TITLE = {Algebraic versus rigid cohomology with logarithmic coefficients},
BOOKTITLE = {Barsotti {S}ymposium in {A}lgebraic {G}eometry},
VENUE={{A}bano {T}erme, 1991},
SERIES = {Perspect. Math.},
VOLUME = {15},
PAGES = {11--50},
PUBLISHER = {Academic Press},
ADDRESS = {San Diego, CA},
YEAR = {1994},
MRCLASS = {14F30 (12H25 14G20)},
MRNUMBER = {1307391},
MRREVIEWER = {Yves Andr{é}},
ZBLNUMBER = {0833.14010},
} -
[Be0] P. Berthelot, "Cohomologie rigide et théorie des $\mathcal{D}$-modules," in $p$-Adic Analysis, New York: Springer-Verlag, 1990, vol. 1454, pp. 80-124.
@incollection {Be0, MRKEY = {1094848},
AUTHOR = {Berthelot, Pierre},
TITLE = {Cohomologie rigide et théorie des {$\mathcal{D}$}-modules},
BOOKTITLE = {{$p$}-Adic Analysis},
VENUE={{T}rento, 1989},
SERIES = {Lecture Notes in Math.},
VOLUME = {1454},
PAGES = {80--124},
PUBLISHER = {Springer-Verlag},
ADDRESS = {New York},
YEAR = {1990},
MRCLASS = {14F30 (14D15 14F10 16S32)},
MRNUMBER = {1094848},
MRREVIEWER = {Luis Narv{á}ez Macarro},
DOI = {10.1007/BFb0091135},
ZBLNUMBER = {0722.14008},
} -
[Be] P. Berthelot, Cohomologie rigide et cohomologie rigide à supports propres. Première Partie, 1996.
@misc{Be,
author={Berthelot, Pierre},
TITLE = {Cohomologie rigide et cohomologie rigide à supports propres. Première Partie},
NOTE={preprint, Université de Rennes},
YEAR={1996},
URL = {http://perso.univ-rennes1.fr/pierre.berthelot/publis/Cohomologie_Rigide_I.pdf},
} -
[Be1] P. Berthelot, "$\mathcal{D}$-modules arithmétiques. I. Opérateurs différentiels de niveau fini," Ann. Sci. École Norm. Sup., vol. 29, iss. 2, pp. 185-272, 1996.
@article {Be1, MRKEY = {1373933},
AUTHOR = {Berthelot, Pierre},
TITLE = {{$\mathcal{D}$}-modules arithmétiques. {I}. {O}pérateurs différentiels de niveau fini},
JOURNAL = {Ann. Sci. École Norm. Sup.},
FJOURNAL = {Annales Scientifiques de l'École Normale Supérieure. Quatrième Série},
VOLUME = {29},
YEAR = {1996},
NUMBER = {2},
PAGES = {185--272},
ISSN = {0012-9593},
CODEN = {ASENAH},
MRCLASS = {14F10 (14F30 14G20)},
MRNUMBER = {1373933},
MRREVIEWER = {Johan de Jong},
URL = {http://www.numdam.org/item?id=ASENS_1996_4_29_2_185_0},
ZBLNUMBER = {0886.14004},
} -
[Be2] P. Berthelot, $\mathcal{D}$-Modules Arithmétiques. II. Descente par Frobenius, , 2000, vol. 81.
@book{Be2,
author = {Berthelot, Pierre},
TITLE = {$\mathcal{D}$-Modules Arithmétiques. {I}{I}. {D}escente par {F}robenius},
SERIES={Mém. Soc. Math. Fr. (N.S.)},
VOLUME={81},
YEAR={2000},
PAGES={vi+136},
MRNUMBER = {1775613},
ZBLNUMBER = {0948.14017},
URL = {http://www.numdam.org/item?id=MSMF_2000_2_81__1_0},
} -
[Beintro2] P. Berthelot, "Introduction à la théorie arithmétique des $\mathcal{D}$-modules," in Cohomologies $p$-Adiques et Applications Arithmétiques, II, , 2002, vol. 279, pp. 1-80.
@incollection {Beintro2, MRKEY = {1922828},
AUTHOR = {Berthelot, Pierre},
TITLE = {Introduction à la théorie arithmétique des {$\mathcal{D}$}-modules},
BOOKTITLE = {Cohomologies $p$-Adiques et Applications Arithm{é}tiques, II},
SERIES = {Astérisque},
FJOURNAL = {Astérisque},
VOLUME = {279},
YEAR = {2002},
PAGES = {1--80},
ISSN = {0303-1179},
MRCLASS = {14F10 (13N10 14F30 14F40 14G22 16S32 32C38)},
MRNUMBER = {1922828},
MRREVIEWER = {Elmar Grosse-Kl{ö}nne},
ZBLNUMBER = {1098.14010},
} -
[BGR] S. Bosch, U. Güntzer, and R. Remmert, Non-Archimedean Analysis, New York: Springer-Verlag, 1984, vol. 261.
@book {BGR, MRKEY = {0746961},
AUTHOR = {Bosch, S. and G{ü}ntzer, U. and Remmert, R.},
TITLE = {Non-{A}rchimedean Analysis},
SERIES = {Grundlehren Math. Wiss.},
VOLUME = {261},
NOTE = {A systematic approach to rigid analytic geometry},
PUBLISHER = {Springer-Verlag},
ADDRESS = {New York},
YEAR = {1984},
PAGES = {xii+436},
ISBN = {3-540-12546-9},
MRCLASS = {32K10 (30G05 46P05)},
MRNUMBER = {0746961},
MRREVIEWER = {W. Bartenwerfer},
ZBLNUMBER = {0539.14017},
} -
[carosurcoherent] D. Caro, "$\mathcal{D}$ modules arithmétiques surcohérents. Application aux fonctions $L$," Ann. Inst. Fourier $($Grenoble$)$, vol. 54, iss. 6, pp. 1943-1996, 2004.
@article {carosurcoherent, MRKEY = {2134230},
AUTHOR = {Caro, Daniel},
TITLE = {{$\mathcal{D}$} modules arithmétiques surcohérents. {A}pplication aux fonctions {$L$}},
JOURNAL = {Ann. Inst. Fourier $($Grenoble$)$},
FJOURNAL = {Université de Grenoble. Annales de l'Institut Fourier},
VOLUME = {54},
YEAR = {2004},
NUMBER = {6},
PAGES = {1943--1996},
ISSN = {0373-0956},
CODEN = {AIFUA7},
MRCLASS = {14F30 (11G25 14G10)},
MRNUMBER = {2134230},
MRREVIEWER = {Ricardo Garc{\'ı}a L{ó}pez},
URL = {http://aif.cedram.org/item?id=AIF_2004__54_6_1943_0},
ZBLNUMBER = {1129.14030},
} -
[carodevissgesurcoh] D. Caro, "Dévissages des $F$-complexes de $\mathcal{D}$-modules arithmétiques en $F$-isocristaux surconvergents," Invent. Math., vol. 166, iss. 2, pp. 397-456, 2006.
@article {carodevissgesurcoh, MRKEY = {2249804},
AUTHOR = {Caro, Daniel},
TITLE = {Dévissages des {$F$}-complexes de {$\mathcal{D}$}-modules arithmétiques en {$F$}-isocristaux surconvergents},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventiones Mathematicae},
VOLUME = {166},
YEAR = {2006},
NUMBER = {2},
PAGES = {397--456},
ISSN = {0020-9910},
CODEN = {INVMBH},
MRCLASS = {14F10 (14F30)},
MRNUMBER = {2249804},
MRREVIEWER = {Laurent N. Berger},
DOI = {10.1007/s00222-006-0517-9},
ZBLNUMBER = {1114.14011},
} -
[carocourbe-nouveau] D. Caro, "Fonctions $L$ associées aux $\mathcal{D}$-modules arithmétiques. Cas des courbes," Compos. Math., vol. 142, iss. 1, pp. 169-206, 2006.
@article {carocourbe-nouveau, MRKEY = {2197408},
AUTHOR = {Caro, Daniel},
TITLE = {Fonctions {$L$} associées aux {$\mathcal{D}$}-modules arithmétiques. {C}as des courbes},
JOURNAL = {Compos. Math.},
FJOURNAL = {Compositio Mathematica},
VOLUME = {142},
YEAR = {2006},
NUMBER = {1},
PAGES = {169--206},
ISSN = {0010-437X},
MRCLASS = {14F10 (14F30)},
MRNUMBER = {2197408},
DOI = {10.1112/S0010437X05001880},
ZBLNUMBER = {1167.14012},
} -
[caro-2006-surcoh-surcv] D. Caro, "$F$-isocristaux surconvergents et surcohérence différentielle," Invent. Math., vol. 170, iss. 3, pp. 507-539, 2007.
@article {caro-2006-surcoh-surcv, MRKEY = {2357501},
AUTHOR = {Caro, Daniel},
TITLE = {{$F$}-isocristaux surconvergents et surcohérence différentielle},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventiones Mathematicae},
VOLUME = {170},
YEAR = {2007},
NUMBER = {3},
PAGES = {507--539},
ISSN = {0020-9910},
CODEN = {INVMBH},
MRCLASS = {14F30},
MRNUMBER = {2357501},
MRREVIEWER = {Laurent N. Berger},
DOI = {10.1007/s00222-007-0070-1},
ZBLNUMBER = {1203.14025},
} -
[caro-stab-prod-tens] D. Caro, Sur la stabilité par produits tensoriels des $F$-complexes de $\mathcal{D}$-modules arithmétiques, 2007.
@misc{caro-stab-prod-tens,
author={Caro, Daniel},
TITLE = {Sur la stabilité par produits tensoriels des $F$-complexes de {$\mathcal{D}$}-modules arithmétiques},
URL = {http://www.math.unicaen.fr/~caro/#prepublication},
YEAR={2007},
} -
[carosurholonome] D. Caro, "$\mathcal{D}$-modules arithmétiques surholonomes," Ann. Sci. École Norm. Supér., vol. 42, iss. 1, pp. 141-192, 2009.
@article {carosurholonome, MRKEY = {2518895},
AUTHOR = {Caro, Daniel},
TITLE = {{$\mathcal{D}$}-modules arithmétiques surholonomes},
JOURNAL = {Ann. Sci. École Norm. Supér.},
FJOURNAL = {Annales Scientifiques de l'École Normale Supérieure. Quatrième Série},
VOLUME = {42},
YEAR = {2009},
NUMBER = {1},
PAGES = {141--192},
ISSN = {0012-9593},
MRCLASS = {14F10 (14G15)},
MRNUMBER = {2518895},
MRREVIEWER = {Luisa Fiorot},
ZBLNUMBER = {1168.14013},
} -
[caro-construction] D. Caro, "$\mathcal{D}$-modules arithmétiques associés aux isocristaux surconvergents. Cas lisse," Bull. Soc. Math. France, vol. 137, iss. 4, pp. 453-543, 2009.
@article {caro-construction, MRKEY = {2572180},
AUTHOR = {Caro, Daniel},
TITLE = {{$\mathcal{D}$}-modules arithmétiques associés aux isocristaux surconvergents. {C}as lisse},
JOURNAL = {Bull. Soc. Math. France},
FJOURNAL = {Bulletin de la Société Mathématique de France},
VOLUME = {137},
YEAR = {2009},
NUMBER = {4},
PAGES = {453--543},
ISSN = {0037-9484},
CODEN = {BSMFAA},
MRCLASS = {14F10 (14F30)},
MRNUMBER = {2572180},
MRREVIEWER = {Luisa Fiorot},
ZBLNUMBER = {05641662},
URL = {http://smf4.emath.fr/Publications/Bulletin/137/html/smf_bull_137_453-543.php},
} -
[carolog-iso-hol] D. Caro, "Log-isocristaux surconvergents et holonomie," Compos. Math., vol. 145, iss. 6, pp. 1465-1503, 2009.
@article {carolog-iso-hol, MRKEY = {2575091},
AUTHOR = {Caro, Daniel},
TITLE = {Log-isocristaux surconvergents et holonomie},
JOURNAL = {Compos. Math.},
FJOURNAL = {Compositio Mathematica},
VOLUME = {145},
YEAR = {2009},
NUMBER = {6},
PAGES = {1465--1503},
ISSN = {0010-437X},
MRCLASS = {14F30 (14F10)},
MRNUMBER = {2575091},
MRREVIEWER = {Adolfo Quir{ó}s},
DOI = {10.1112/S0010437X09004199},
ZBLNUMBER = {05654707},
} -
[carocaract-surcoh] D. Caro, "Une caractérisation de la surcohérence," J. Math. Sci. Univ. Tokyo, vol. 16, iss. 1, pp. 1-21, 2009.
@article {carocaract-surcoh, MRKEY = {2548931},
AUTHOR = {Caro, Daniel},
TITLE = {Une caractérisation de la surcohérence},
JOURNAL = {J. Math. Sci. Univ. Tokyo},
FJOURNAL = {The University of Tokyo. Journal of Mathematical Sciences},
VOLUME = {16},
YEAR = {2009},
NUMBER = {1},
PAGES = {1--21},
ISSN = {1340-5705},
MRCLASS = {14F30 (14F10 14F40)},
MRNUMBER = {2548931},
MRREVIEWER = {Feng-Wen An},
ZBLNUMBER = {1213.14041},
} -
[descent] B. Chiarellotto and N. Tsuzuki, "Cohomological descent of rigid cohomology for étale coverings," Rend. Sem. Mat. Univ. Padova, vol. 109, pp. 63-215, 2003.
@article {descent, MRKEY = {1997987},
AUTHOR = {Chiarellotto, Bruno and Tsuzuki, Nobuo},
TITLE = {Cohomological descent of rigid cohomology for étale coverings},
JOURNAL = {Rend. Sem. Mat. Univ. Padova},
FJOURNAL = {Rendiconti del Seminario Matematico della Università di Padova. The Mathematical Journal of the University of Padova},
VOLUME = {109},
YEAR = {2003},
PAGES = {63--215},
ISSN = {0041-8994},
MRCLASS = {14F30 (14F43 14G22)},
MRNUMBER = {1997987},
MRREVIEWER = {Elmar Grosse-Kl{ö}nne},
ZBLNUMBER = {1167.14306},
URL = { http://www.numdam.org/item?id=RSMUP_2003__109__63_0},
} -
[transfer] G. Christol, "Un théorème de transfert pour les disques singuliers réguliers," in $p$-Adic Cohomology, , 1984, vol. 119-120, p. 5, 151-168.
@incollection {transfer, MRKEY = {0773091},
AUTHOR = {Christol, Gilles},
TITLE = {Un théorème de transfert pour les disques singuliers réguliers},
BOOKTITLE = {$p$-Adic Cohomology},
SERIES = {Astérisque},
FJOURNAL = {Astérisque},
VOLUME = {119-120},
YEAR = {1984},
PAGES = {5, 151--168},
ISSN = {0303-1179},
MRCLASS = {12H25 (11S80 34A25)},
MRNUMBER = {0773091},
MRREVIEWER = {W. Bartenwerfer},
ZBLNUMBER = {0553.12014},
} -
[crew-finite] R. Crew, "Finiteness theorems for the cohomology of an overconvergent isocrystal on a curve," Ann. Sci. École Norm. Sup., vol. 31, iss. 6, pp. 717-763, 1998.
@article {crew-finite, MRKEY = {1664230},
AUTHOR = {Crew, Richard},
TITLE = {Finiteness theorems for the cohomology of an overconvergent isocrystal on a curve},
JOURNAL = {Ann. Sci. École Norm. Sup.},
FJOURNAL = {Annales Scientifiques de l'École Normale Supérieure. Quatrième Série},
VOLUME = {31},
YEAR = {1998},
NUMBER = {6},
PAGES = {717--763},
ISSN = {0012-9593},
CODEN = {ASENAH},
MRCLASS = {14F30 (14F20)},
MRNUMBER = {1664230},
MRREVIEWER = {Nobuo Tsuzuki},
DOI = {10.1016/S0012-9593(99)80001-9},
ZBLNUMBER = {0943.14008},
} -
[crew-arith-D-mod-curve] R. Crew, "Arithmetic $\mathcal{D}$-modules on a formal curve," Math. Ann., vol. 336, iss. 2, pp. 439-448, 2006.
@article {crew-arith-D-mod-curve, MRKEY = {2244380},
AUTHOR = {Crew, Richard},
TITLE = {Arithmetic {$\mathcal{D}$}-modules on a formal curve},
JOURNAL = {Math. Ann.},
FJOURNAL = {Mathematische Annalen},
VOLUME = {336},
YEAR = {2006},
NUMBER = {2},
PAGES = {439--448},
ISSN = {0025-5831},
CODEN = {MAANA},
MRCLASS = {14F10 (14F30 14G20)},
MRNUMBER = {2244380},
MRREVIEWER = {Martin C. Olsson},
DOI = {10.1007/s00208-006-0011-0},
ZBLNUMBER = {1131.14018},
} -
[dejong] A. J. de Jong, "Smoothness, semi-stability and alterations," Inst. Hautes Études Sci. Publ. Math., vol. 83, pp. 51-93, 1996.
@article {dejong, MRKEY = {1423020},
AUTHOR = {de Jong, A. J.},
TITLE = {Smoothness, semi-stability and alterations},
JOURNAL = {Inst. Hautes Études Sci. Publ. Math.},
FJOURNAL = {Institut des Hautes Études Scientifiques. Publications Mathématiques},
VOLUME = {83},
YEAR = {1996},
PAGES = {51--93},
ISSN = {0073-8301},
CODEN = {PMIHA6},
MRCLASS = {14E15 (14B05 14H10)},
MRNUMBER = {1423020},
MRREVIEWER = {Marko Roczen},
URL = {http://www.numdam.org/item?id=PMIHES_1996__83__51_0},
ZBLNUMBER = {0916.14005},
} -
[dgs] B. Dwork, G. Gerotto, and F. J. Sullivan, An introduction to $G$-functions, Princeton, NJ: Princeton Univ. Press, 1994.
@book {dgs, MRKEY = {1274045},
AUTHOR = {Dwork, Bernard and Gerotto, Giovanni and Sullivan, Francis J.},
TITLE = {An introduction to {$G$}-functions},
SERIES = {Annals of Mathematics Studies},
NUMBER = {133},
PUBLISHER = {Princeton Univ. Press},
ADDRESS = {Princeton, NJ},
YEAR = {1994},
PAGES = {xxii+323},
ISBN = {0-691-03681-0},
MRCLASS = {12H25 (11S80 12J25 13F25 14G20 34A99)},
MRNUMBER = {1274045},
MRREVIEWER = {Adolfo Quir{ó}s},
ZBLNUMBER = {0830.12004},
} -
[kedlayasemi-stable] K. S. Kedlaya, "Semistable reduction for overconvergent $F$-isocrystals on a curve," Math. Res. Lett., vol. 10, iss. 2-3, pp. 151-159, 2003.
@article {kedlayasemi-stable, MRKEY = {1981892},
AUTHOR = {Kedlaya, Kiran S.},
TITLE = {Semistable reduction for overconvergent {$F$}-isocrystals on a curve},
JOURNAL = {Math. Res. Lett.},
FJOURNAL = {Mathematical Research Letters},
VOLUME = {10},
YEAR = {2003},
NUMBER = {2-3},
PAGES = {151--159},
ISSN = {1073-2780},
MRCLASS = {12H25 (14F30 14G20)},
MRNUMBER = {1981892},
MRREVIEWER = {Christine Noot-Huyghe},
ZBLNUMBER = {1057.14024},
URL = {http://www.mrlonline.org/mrl/2003-010-002/2003-010-002-002.html},
} -
[kedlayafull-faithful] K. S. Kedlaya, "Full faithfulness for overconvergent $F$-isocrystals," in Geometric Aspects of Dwork Theory. Vol. I, II, Walter de Gruyter, Berlin, 2004, pp. 819-835.
@incollection {kedlayafull-faithful, MRKEY = {2099088},
AUTHOR = {Kedlaya, Kiran S.},
TITLE = {Full faithfulness for overconvergent {$F$}-isocrystals},
BOOKTITLE = {Geometric Aspects of {D}work Theory. {V}ol. {I},
{II}},
PAGES = {819--835},
PUBLISHER = {Walter de Gruyter, Berlin},
YEAR = {2004},
MRCLASS = {14F30},
MRNUMBER = {2099088},
MRREVIEWER = {Elmar Grosse-Kl{ö}nne},
ZBLNUMBER = {1087.14018},
} -
[Kedlaya-coveraffinebis] K. S. Kedlaya, "More étale covers of affine spaces in positive characteristic," J. Algebraic Geom., vol. 14, iss. 1, pp. 187-192, 2005.
@article {Kedlaya-coveraffinebis, MRKEY = {2092132},
AUTHOR = {Kedlaya, Kiran S.},
TITLE = {More étale covers of affine spaces in positive characteristic},
JOURNAL = {J. Algebraic Geom.},
FJOURNAL = {Journal of Algebraic Geometry},
VOLUME = {14},
YEAR = {2005},
NUMBER = {1},
PAGES = {187--192},
ISSN = {1056-3911},
MRCLASS = {14E20 (13A35)},
MRNUMBER = {2092132},
MRREVIEWER = {Gordon Heier},
DOI = {10.1090/S1056-3911-04-00381-9},
ZBLNUMBER = {1065.14020},
} -
[kedlaya-semistableI] K. S. Kedlaya, "Semistable reduction for overconvergent $F$-isocrystals. I. Unipotence and logarithmic extensions," Compos. Math., vol. 143, iss. 5, pp. 1164-1212, 2007.
@article {kedlaya-semistableI, MRKEY = {2360314},
AUTHOR = {Kedlaya, Kiran S.},
TITLE = {Semistable reduction for overconvergent {$F$}-isocrystals. {I}. {U}nipotence and logarithmic extensions},
JOURNAL = {Compos. Math.},
FJOURNAL = {Compositio Mathematica},
VOLUME = {143},
YEAR = {2007},
NUMBER = {5},
PAGES = {1164--1212},
ISSN = {0010-437X},
MRCLASS = {14F30 (14F40)},
MRNUMBER = {2360314},
MRREVIEWER = {Laurent N. Berger},
DOI = {10.1112/S0010437X07002886},
ZBLNUMBER = {1144.14012},
} -
[kedlaya-semistableII] K. S. Kedlaya, "Semistable reduction for overconvergent $F$-isocrystals. II. A valuation-theoretic approach," Compos. Math., vol. 144, iss. 3, pp. 657-672, 2008.
@article {kedlaya-semistableII, MRKEY = {2422343},
AUTHOR = {Kedlaya, Kiran S.},
TITLE = {Semistable reduction for overconvergent {$F$}-isocrystals. {II}. {A} valuation-theoretic approach},
JOURNAL = {Compos. Math.},
FJOURNAL = {Compositio Mathematica},
VOLUME = {144},
YEAR = {2008},
NUMBER = {3},
PAGES = {657--672},
ISSN = {0010-437X},
MRCLASS = {14F30 (14F40)},
MRNUMBER = {2422343},
MRREVIEWER = {Laurent N. Berger},
DOI = {10.1112/S0010437X07003296},
ZBLNUMBER = {1153.14015},
} -
[kedlaya-semistableIII] K. S. Kedlaya, "Semistable reduction for overconvergent $F$-isocrystals. III. Local semistable reduction at monomial valuations," Compos. Math., vol. 145, iss. 1, pp. 143-172, 2009.
@article {kedlaya-semistableIII, MRKEY = {2480498},
AUTHOR = {Kedlaya, Kiran S.},
TITLE = {Semistable reduction for overconvergent {$F$}-isocrystals. {III}. {L}ocal semistable reduction at monomial valuations},
JOURNAL = {Compos. Math.},
FJOURNAL = {Compositio Mathematica},
VOLUME = {145},
YEAR = {2009},
NUMBER = {1},
PAGES = {143--172},
ISSN = {0010-437X},
MRCLASS = {14F30 (14F40)},
MRNUMBER = {2480498},
MRREVIEWER = {Marco A. Garuti},
DOI = {10.1112/S0010437X08003783},
ZBLNUMBER = {1184.14031},
} -
[kedlaya-semistableIV] K. S. Kedlaya, "Semistable reduction for overconvergent $F$-isocrystals, IV: local semistable reduction at nonmonomial valuations," Compos. Math., vol. 147, iss. 2, pp. 467-523, 2011.
@article {kedlaya-semistableIV, MRKEY = {2776611},
AUTHOR = {Kedlaya, Kiran S.},
TITLE = {Semistable reduction for overconvergent {$F$}-isocrystals, {IV}: local semistable reduction at nonmonomial valuations},
JOURNAL = {Compos. Math.},
FJOURNAL = {Compositio Mathematica},
VOLUME = {147},
YEAR = {2011},
NUMBER = {2},
PAGES = {467--523},
ISSN = {0010-437X},
MRCLASS = {14F30 (14F40)},
MRNUMBER = {2776611},
MRREVIEWER = {Marco A. Garuti},
DOI = {10.1112/S0010437X10005142},
ZBLNUMBER = {1230.14023},
} -
[quasistein] R. Kiehl, "Theorem A und Theorem B in der nichtarchimedischen Funktionentheorie," Invent. Math., vol. 2, pp. 256-273, 1967.
@article {quasistein, MRKEY = {0210949},
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},
ZBLNUMBER = {0202.20201},
} -
[LeStum-book-isoc] B. Le Stum, Rigid cohomology, Cambridge: Cambridge Univ. Press, 2007.
@book {LeStum-book-isoc, MRKEY = {2358812},
AUTHOR = {Le Stum, Bernard},
TITLE = {Rigid cohomology},
SERIES = {Cambridge Tracts in Mathematics},
NUMBER = {172},
PUBLISHER = {Cambridge Univ. Press},
ADDRESS = {Cambridge},
YEAR = {2007},
PAGES = {xvi+319},
ISBN = {978-0-521-87524-0},
MRCLASS = {14F30 (14G22)},
MRNUMBER = {2358812},
MRREVIEWER = {Lorenzo Ramero},
DOI = {10.1017/CBO9780511543128},
ZBLNUMBER = {1131.14001},
} -
[nagatalocal] M. Nagata, Local Rings, New York: Interscience Publishers a division of John Wiley & Sons, 1962, vol. 13.
@book {nagatalocal, MRKEY = {0155856},
AUTHOR = {Nagata, Masayoshi},
TITLE = {Local Rings},
SERIES = {Interscience Tracts Pure Appl. Math},
VOLUME={13},
PUBLISHER = {Interscience Publishers a division of John Wiley \& Sons},
ADDRESS={New York},
YEAR = {1962},
PAGES = {xiii+234},
MRCLASS = {13.95 (16.00)},
MRNUMBER = {0155856},
MRREVIEWER = {R. C. Hartshorne},
ZBLNUMBER = {0123.03402},
} -
[Huyghe-Trihan] C. Noot-Huyghe and F. Trihan, "Sur l’holonomie de $\mathcal{D}$-modules arithmétiques associés à des $F$-isocristaux surconvergents sur des courbes lisses," Ann. Fac. Sci. Toulouse Math., vol. 16, iss. 3, pp. 611-634, 2007.
@article {Huyghe-Trihan, MRKEY = {2379054},
AUTHOR = {Noot-Huyghe, Christine and Trihan, Fabien},
TITLE = {Sur l'holonomie de {$\mathcal{D}$}-modules arithmétiques associés à des {$F$}-isocristaux surconvergents sur des courbes lisses},
JOURNAL = {Ann. Fac. Sci. Toulouse Math.},
FJOURNAL = {Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série 6},
VOLUME = {16},
YEAR = {2007},
NUMBER = {3},
PAGES = {611--634},
ISSN = {0240-2963},
MRCLASS = {14F10 (14F30)},
MRNUMBER = {2379054},
MRREVIEWER = {Feng-Wen An},
DOI = {10.5802/afst.1161},
ZBLNUMBER = {1213.14043},
} -
[Shiho-log-isocI] A. Shiho, "Crystalline fundamental groups. I. Isocrystals on log crystalline site and log convergent site," J. Math. Sci. Univ. Tokyo, vol. 7, iss. 4, pp. 509-656, 2000.
@article {Shiho-log-isocI, MRKEY = {1800845},
AUTHOR = {Shiho, Atsushi},
TITLE = {Crystalline fundamental groups. {I}. {I}socrystals on log crystalline site and log convergent site},
JOURNAL = {J. Math. Sci. Univ. Tokyo},
FJOURNAL = {The University of Tokyo. Journal of Mathematical Sciences},
VOLUME = {7},
YEAR = {2000},
NUMBER = {4},
PAGES = {509--656},
ISSN = {1340-5705},
MRCLASS = {14F30 (14F35 14F40)},
MRNUMBER = {1800845},
MRREVIEWER = {Bruno Chiarellotto},
ZBLNUMBER = {0984.14009},
} -
[Shi1] A. Shiho, "Crystalline fundamental groups. II. Log convergent cohomology and rigid cohomology," J. Math. Sci. Univ. Tokyo, vol. 9, iss. 1, pp. 1-163, 2002.
@article {Shi1, MRKEY = {1889223},
AUTHOR = {Shiho, Atsushi},
TITLE = {Crystalline fundamental groups. {II}. {L}og convergent cohomology and rigid cohomology},
JOURNAL = {J. Math. Sci. Univ. Tokyo},
FJOURNAL = {The University of Tokyo. Journal of Mathematical Sciences},
VOLUME = {9},
YEAR = {2002},
NUMBER = {1},
PAGES = {1--163},
ISSN = {1340-5705},
MRCLASS = {14F30 (14F35 14F40)},
MRNUMBER = {1889223},
MRREVIEWER = {Bruno Chiarellotto},
ZBLNUMBER= {1057.14025},
} -
[Tsu1] N. Tsuzuki, "On the Gysin isomorphism of rigid cohomology," Hiroshima Math. J., vol. 29, iss. 3, pp. 479-527, 1999.
@article {Tsu1, MRKEY = {1728610},
AUTHOR = {Tsuzuki, Nobuo},
TITLE = {On the {G}ysin isomorphism of rigid cohomology},
JOURNAL = {Hiroshima Math. J.},
FJOURNAL = {Hiroshima Mathematical Journal},
VOLUME = {29},
YEAR = {1999},
NUMBER = {3},
PAGES = {479--527},
ISSN = {0018-2079},
CODEN = {HMTJAD},
MRCLASS = {14F30 (14F40)},
MRNUMBER = {1728610},
MRREVIEWER = {Bruno Chiarellotto},
URL = {http://projecteuclid.org/euclid.hmj/1206124853},
ZBLNUMBER = {1019.14007},
} -
[Tsu-mono] N. Tsuzuki, "Morphisms of $F$-isocrystals and the finite monodromy theorem for unit-root $F$-isocrystals," Duke Math. J., vol. 111, iss. 3, pp. 385-418, 2002.
@article {Tsu-mono, MRKEY = {1885826},
AUTHOR = {Tsuzuki, Nobuo},
TITLE = {Morphisms of {$F$}-isocrystals and the finite monodromy theorem for unit-root {$F$}-isocrystals},
JOURNAL = {Duke Math. J.},
FJOURNAL = {Duke Mathematical Journal},
VOLUME = {111},
YEAR = {2002},
NUMBER = {3},
PAGES = {385--418},
ISSN = {0012-7094},
CODEN = {DUMJAO},
MRCLASS = {14F30 (11G25 14F10)},
MRNUMBER = {1885826},
MRREVIEWER = {Laurent N. Berger},
DOI = {10.1215/S0012-7094-02-11131-4},
ZBLNUMBER = {1055.14022},
} -
[virrion] A. Virrion, "Dualité locale et holonomie pour les $\mathcal{D}$-modules arithmétiques," Bull. Soc. Math. France, vol. 128, iss. 1, pp. 1-68, 2000.
@article {virrion, MRKEY = {1765829},
AUTHOR = {Virrion, Anne},
TITLE = {Dualité locale et holonomie pour les {$\mathcal{D}$}-modules arithmétiques},
JOURNAL = {Bull. Soc. Math. France},
FJOURNAL = {Bulletin de la Société Mathématique de France},
VOLUME = {128},
YEAR = {2000},
NUMBER = {1},
PAGES = {1--68},
ISSN = {0037-9484},
CODEN = {BSMFAA},
MRCLASS = {14F30},
MRNUMBER = {1765829},
MRREVIEWER = {Christine Noot-Huyghe},
URL = {http://smf4.emath.fr/Publications/Bulletin/128/html/smf_bull_128_1-68.html},
ZBLNUMBER = {0955.14015},
}
Full Article