Abstract
We apply automorphy lifting techniques to establish new cases of symmetric power functoriality for Hilbert modular forms of regular algebraic weight. The proof is based on a novel application of an automorphy lifting theorem for residually reducible Galois representations.
-
[Art12] J. Arthur, The Endoscopic Classification of Representations. Orthogonal and Symplectic Groups, Providence, RI: Amer. Math. Soc., 2013, vol. 61.
@book{Art12, mrkey = {3135650},
author = {Arthur, James},
title = {The Endoscopic Classification of Representations. Orthogonal and Symplectic Groups},
series = {Amer. Math. Soc. Colloq. Publ.s},
volume = {61},
publisher = {Amer. Math. Soc.},
address = {Providence, RI},
year = {2013},
pages = {xviii+590},
isbn = {978-0-8218-4990-3},
mrclass = {22E55 (11F66 11R37 20G25 22E50)},
mrnumber = {3135650},
zblnumber = {06231010},
} -
[Bel06]
J. Bella"iche and P. Graftieaux, "Augmentation du niveau pour ${ U}(3)$," Amer. J. Math., vol. 128, iss. 2, pp. 271-309, 2006.
@article{Bel06, mrkey = {2214894},
author = {Bella{ï}che, Jo{ë}l and Graftieaux, Phillipe},
title = {Augmentation du niveau pour {${\rm U}(3)$}},
journal = {Amer. J. Math.},
fjournal = {American Journal of Mathematics},
volume = {128},
year = {2006},
number = {2},
pages = {271--309},
issn = {0002-9327},
coden = {AJMAAN},
mrclass = {11F70 (22E55)},
mrnumber = {2214894},
mrreviewer = {Jacques Tilouine},
doi = {10.1353/ajm.2006.0009},
zblnumber = {1135.11025},
} -
[Bar10]
T. Barnet-Lamb, T. Gee, D. Geraghty, and R. Taylor, "Potential automorphy and change of weight," Ann. of Math., vol. 179, iss. 2, pp. 501-609, 2014.
@article{Bar10, mrkey = {3152941},
author = {Barnet-Lamb, Thomas and Gee, Toby and Geraghty, David and Taylor, Richard},
title = {Potential automorphy and change of weight},
journal = {Ann. of Math.},
fjournal = {Annals of Mathematics. Second Series},
volume = {179},
year = {2014},
number = {2},
pages = {501--609},
issn = {0003-486X},
mrclass = {11F33},
mrnumber = {3152941},
mrreviewer = {Wen-Wei Li},
doi = {10.4007/annals.2014.179.2.3},
zblnumber = {06284344},
} -
[Bar09]
T. Barnet-Lamb, D. Geraghty, M. Harris, and R. Taylor, "A family of Calabi-Yau varieties and potential automorphy II," Publ. Res. Inst. Math. Sci., vol. 47, iss. 1, pp. 29-98, 2011.
@article{Bar09, mrkey = {2827723},
author = {Barnet-Lamb, Tom and Geraghty, David and Harris, Michael and Taylor, Richard},
title = {A family of {C}alabi-{Y}au varieties and potential automorphy {II}},
journal = {Publ. Res. Inst. Math. Sci.},
fjournal = {Publications of the Research Institute for Mathematical Sciences},
volume = {47},
year = {2011},
number = {1},
pages = {29--98},
issn = {0034-5318},
mrclass = {11F80 (11F11 11G18 14J32)},
mrnumber = {2827723},
mrreviewer = {Neil P. Dummigan},
doi = {10.2977/PRIMS/31},
zblnumber = {1264.11044},
} -
[Ber12] N. Bergeron, J. Millson, and C. Moeglin, Hodge type theorems for arithmetic manifolds associated to orthogonal groups.
@misc{Ber12,
author = {Bergeron, N. and Millson, J. and M{\oe}glin, C.},
title = {Hodge type theorems for arithmetic manifolds associated to orthogonal groups},
arxiv = {1110.3049},
} -
[Bor76]
A. Borel, "Admissible representations of a semi-simple group over a local field with vectors fixed under an Iwahori subgroup," Invent. Math., vol. 35, pp. 233-259, 1976.
@article{Bor76, mrkey = {0444849},
author = {Borel, Armand},
title = {Admissible representations of a semi-simple group over a local field with vectors fixed under an {I}wahori subgroup},
journal = {Invent. Math.},
fjournal = {Inventiones Mathematicae},
volume = {35},
year = {1976},
pages = {233--259},
issn = {0020-9910},
mrclass = {22E50 (20G05)},
mrnumber = {0444849},
mrreviewer = {Allan J. Silberger},
doi = {10.1007/BF01390139},
zblnumber = {0334.22012},
} -
[Bru72]
F. Bruhat and J. Tits, "Groupes réductifs sur un corps local," Inst. Hautes Études Sci. Publ. Math., vol. 41, pp. 5-251, 1972.
@article{Bru72, mrkey = {0327923},
author = {Bruhat, F. and Tits, J.},
title = {Groupes réductifs sur un corps local},
journal = {Inst. Hautes Études Sci. Publ. Math.},
fjournal = {Institut des Hautes Études Scientifiques. Publications Mathématiques},
VOLUME = {41},
year = {1972},
pages = {5--251},
issn = {0073-8301},
mrclass = {20G25 (22E20)},
mrnumber = {0327923},
mrreviewer = {M. Krusemeyer},
url = {http://www.numdam.org/item?id=PMIHES_1972__41__5_0},
zblnumber = {0254.14017},
} -
[Car79] P. Cartier, "Representations of $p$-adic groups: a survey," in Automorphic Forms, Representations and $L$-Functions, Providence, RI: Amer. Math. Soc., 1979, vol. XXXIII, pp. 111-155.
@incollection{Car79, mrkey = {0546593},
author = {Cartier, P.},
title = {Representations of {$p$}-adic groups: a survey},
booktitle = {Automorphic Forms, Representations and {$L$}-Functions},
venue = {{P}roc. {S}ympos. {P}ure {M}ath., {O}regon {S}tate {U}niv., {C}orvallis, {O}re., 1977, {P}art 1},
series = {Proc. Sympos. Pure Math.},
volume = {XXXIII},
pages = {111--155},
publisher = {Amer. Math. Soc.},
address = {Providence, RI},
year = {1979},
mrclass = {22E50},
mrnumber = {0546593},
mrreviewer = {Allan J. Silberger},
zblnumber = {0421.22010},
} -
[Car12]
A. Caraiani, "Local-global compatibility and the action of monodromy on nearby cycles," Duke Math. J., vol. 161, iss. 12, pp. 2311-2413, 2012.
@article{Car12, mrkey = {2972460},
author = {Caraiani, Ana},
title = {Local-global compatibility and the action of monodromy on nearby cycles},
journal = {Duke Math. J.},
fjournal = {Duke Mathematical Journal},
volume = {161},
year = {2012},
number = {12},
pages = {2311--2413},
issn = {0012-7094},
coden = {DUMJAO},
mrclass = {22E57 (11F70 11F80 11R39 14G35)},
mrnumber = {2972460},
mrreviewer = {Kai-Wen Lan},
doi = {10.1215/00127094-1723706},
zblnumber = {06095601},
} -
[Cas95]
W. Casselman, Introduction to the theory of admissible representations of $p$-adic reductive groups.
@misc{Cas95,
author = {Casselman, W.},
title = {Introduction to the theory of admissible representations of {$p$}-adic reductive groups},
note = {unpublished draft of 1 {M}ay 1995},
url = {http://www.math.ubc.ca/~cass/research/pdf/p-adic-book.pdf},
} -
[Cas80]
W. Casselman, "The unramified principal series of ${\mathfrak p}$-adic groups. I. The spherical function," Compositio Math., vol. 40, iss. 3, pp. 387-406, 1980.
@article{Cas80, mrkey = {0571057},
author = {Casselman, W.},
title = {The unramified principal series of {${\mathfrak p}$}-adic groups. {I}. {T}he spherical function},
journal = {Compositio Math.},
fjournal = {Compositio Mathematica},
volume = {40},
year = {1980},
number = {3},
pages = {387--406},
issn = {0010-437X},
coden = {CMPMAF},
mrclass = {22E50},
mrnumber = {0571057},
mrreviewer = {Allan J. Silberger},
url = {http://www.numdam.org/item?id=CM_1980__40_3_387_0},
zblnumber = {0472.22004},
} -
[Che13]
G. Chenevier and M. Harris, "Construction of automorphic Galois representations, II," Cambridge Math J., vol. 1, pp. 53-73, 2013.
@article{Che13,
author = {Chenevier, G. and Harris, M.},
title = {Construction of automorphic {G}alois representations, {II}},
journal = {Cambridge Math J.},
VOLUME={1} , YEAR={2013},
PAGES={53--73},
doi = {10.4310/CJM.2013.v1.n1.a2},
ZBLNUMBER = {06266535},
} -
[Clo11a] L. Clozel, M. Harris, and J. Labesse, "Endoscopic transfer," in On the Stabilization of the Trace Formula, Somerville, MA: Int. Press, 2011, vol. 1, pp. 475-496.
@incollection{Clo11a, mrkey = {2856382},
author = {Clozel, Laurent and Harris, Michael and Labesse, Jean-Pierre},
title = {Endoscopic transfer},
booktitle = {On the Stabilization of the Trace Formula},
series = {Stab. Trace Formula Shimura Var. Arith. Appl.},
volume = {1},
pages = {475--496},
publisher = {Int. Press},
address = {Somerville, MA},
year = {2011},
mrclass = {11F70 (22E55)},
mrnumber = {2856382},
zblnumber = {1255.11027},
} -
[Clo08]
L. Clozel, M. Harris, and R. Taylor, "Automorphy for some $l$-adic lifts of automorphic mod $l$ Galois representations," Publ. Math. Inst. Hautes Études Sci., vol. 108, pp. 1-181, 2008.
@article{Clo08, mrkey = {2470687},
author = {Clozel, Laurent and Harris, Michael and Taylor, Richard},
title = {Automorphy for some \hbox{{$l$}-adic} lifts of automorphic mod {$l$} {G}alois representations},
note = {with Appendix A, summarizing unpublished work of Russ Mann, and Appendix B by Marie-France Vign{é}ras},
journal = {Publ. Math. Inst. Hautes Études Sci.},
fjournal = {Publications Mathématiques. Institut de Hautes Études Scientifiques},
volume = {108},
year = {2008},
pages = {1--181},
issn = {0073-8301},
mrclass = {11F80 (11G18 11R34)},
mrnumber = {2470687},
mrreviewer = {Mark Kisin},
doi = {10.1007/s10240-008-0016-1},
zblnumber = {1169.11020},
} -
[Cha10]
P. Chaudouard and G. Laumon, "Le lemme fondamental pondéré. I. Constructions géométriques," Compos. Math., vol. 146, iss. 6, pp. 1416-1506, 2010.
@article{Cha10, mrkey = {2735371},
author = {Chaudouard, Pierre-Henri and Laumon, G{é}rard},
title = {Le lemme fondamental pondéré. {I}. {C}onstructions géométriques},
journal = {Compos. Math.},
fjournal = {Compositio Mathematica},
volume = {146},
year = {2010},
number = {6},
pages = {1416--1506},
issn = {0010-437X},
mrclass = {22E55 (11F70 11F72 11R39 14D23)},
mrnumber = {2735371},
mrreviewer = {Anne-Marie H. Aubert},
doi = {10.1112/S0010437X10004756},
zblnumber = {1206.14026},
} -
[Cha12]
P. Chaudouard and G. Laumon, "Le lemme fondamental pondéré. II. Énoncés cohomologiques," Ann. of Math., vol. 176, iss. 3, pp. 1647-1781, 2012.
@article{Cha12, mrkey = {2979859},
author = {Chaudouard, Pierre-Henri and Laumon, G{é}rard},
title = {Le lemme fondamental pondéré. {II}. \'{E}noncés cohomologiques},
journal = {Ann. of Math.},
fjournal = {Annals of Mathematics. Second Series},
volume = {176},
year = {2012},
number = {3},
pages = {1647--1781},
issn = {0003-486X},
coden = {ANMAAH},
mrclass = {11F70 (11F72 22E50)},
mrnumber = {2979859},
mrreviewer = {Anne-Marie H. Aubert},
doi = {10.4007/annals.2012.176.3.6},
ZBLNUMBER = {1264.11043},
} -
[Clo90a]
L. Clozel, "The fundamental lemma for stable base change," Duke Math. J., vol. 61, iss. 1, pp. 255-302, 1990.
@article{Clo90a, mrkey = {1068388},
author = {Clozel, Laurent},
title = {The fundamental lemma for stable base change},
journal = {Duke Math. J.},
fjournal = {Duke Mathematical Journal},
volume = {61},
year = {1990},
number = {1},
pages = {255--302},
issn = {0012-7094},
coden = {DUMJAO},
mrclass = {22E50},
mrnumber = {1068388},
mrreviewer = {David Manderscheid},
doi = {10.1215/S0012-7094-90-06112-5},
zblnumber = {0731.22011},
} -
[Clo90] L. Clozel, "Motifs et formes automorphes: applications du principe de fonctorialité," in Automorphic Forms, Shimura varieties, and $L$-Functions, Vol. I, Academic Press, Boston, 1990, vol. 10, pp. 77-159.
@incollection{Clo90, mrkey = {1044819},
author = {Clozel, Laurent},
title = {Motifs et formes automorphes: applications du principe de fonctorialité},
booktitle = {Automorphic Forms, {S}himura varieties, and {$L$}-Functions, {V}ol. {I}},
venue = {{A}nn {A}rbor, {MI},
1988},
series = {Perspect. Math.},
volume = {10},
pages = {77--159},
publisher = {Academic Press, Boston},
year = {1990},
mrclass = {11F70 (11F75 11F80 11R39 22E55)},
mrnumber = {1044819},
mrreviewer = {Ernst-Wilhelm Zink},
zblnumber = {0705.11029},
} -
[Clo11] L. Clozel, "Identités de caractères en la place archimédienne," in On the Stabilization of the Trace Formula, Somerville, MA: Int. Press, 2011, vol. 1, pp. 351-367.
@incollection{Clo11, mrkey = {2856375},
author = {Clozel, Laurent},
title = {Identités de caractères en la place archimédienne},
booktitle = {On the Stabilization of the Trace Formula},
series = {Stab. Trace Formula Shimura Var. Arith. Appl.},
volume = {1},
pages = {351--367},
publisher = {Int. Press},
address = {Somerville, MA},
year = {2011},
mrclass = {22E45},
mrnumber = {2856375},
zblnumber = {1255.11027},
} -
[Clo13]
L. Clozel and J. A. Thorne, "Level-raising and symmetric power functoriality, I," Compos. Math., vol. 150, iss. 5, pp. 729-748, 2014.
@article{Clo13, mrkey = {3209793},
author = {Clozel, Laurent and Thorne, Jack A.},
title = {Level-raising and symmetric power functoriality, {I}},
journal = {Compos. Math.},
fjournal = {Compositio Mathematica},
volume = {150},
year = {2014},
number = {5},
pages = {729--748},
issn = {0010-437X},
mrclass = {11F80 (11F03 11F66)},
mrnumber = {3209793},
doi = {10.1112/S0010437X13007653},
zblnumber = {1024.11027},
} -
[Gee11]
T. Gee, "Automorphic lifts of prescribed types," Math. Ann., vol. 350, iss. 1, pp. 107-144, 2011.
@article{Gee11, mrkey = {2785764},
author = {Gee, Toby},
title = {Automorphic lifts of prescribed types},
journal = {Math. Ann.},
fjournal = {Mathematische Annalen},
volume = {350},
year = {2011},
number = {1},
pages = {107--144},
issn = {0025-5831},
coden = {MAANA},
mrclass = {11F80 (11F33 11F41)},
mrnumber = {2785764},
mrreviewer = {James Newton},
doi = {10.1007/s00208-010-0545-z},
zblnumber = {1276.11085},
} -
[Ger09] D. Geraghty, Modularity lifting theorems for ordinary Galois representations.
@misc{Ger09,
author = {Geraghty, David},
title = {Modularity lifting theorems for ordinary {G}alois representations},
note = {preprint},
} -
[goldberg]
D. Goldberg, "Reducibility of generalized principal series representations of ${ U}(2,2)$ via base change," Compositio Math., vol. 86, iss. 3, pp. 245-264, 1993.
@article{goldberg, mrkey = {1219627},
author = {Goldberg, David},
title = {Reducibility of generalized principal series representations of {${\rm U}(2,2)$} via base change},
journal = {Compositio Math.},
fjournal = {Compositio Mathematica},
volume = {86},
year = {1993},
number = {3},
pages = {245--264},
issn = {0010-437X},
coden = {CMPMAF},
mrclass = {22E50},
mrnumber = {1219627},
mrreviewer = {Stephen Gelbart},
url = {http://www.numdam.org/item?id=CM_1993__86_3_245_0},
zblnumber = {0788.22021},
} -
[Gur12] R. Guralnick, Adequacy of representations of finite groups of Lie type.
@misc{Gur12,
author = {Guralnick, R.},
title = {Adequacy of representations of finite groups of {L}ie type},
note = {appendix to ``{A}utomorphy of {S}ymm$^5$({GL}(2)) and base change" by L. Dieulefait},
ARXIV={1208.4128},
} -
[Hen02] G. Henniart, "Une caractérisation de la correspondance de Langlands locale pour ${ GL}(n)$," Bull. Soc. Math. France, vol. 130, iss. 4, pp. 587-602, 2002.
@article{Hen02, mrkey = {1947454},
author = {Henniart, Guy},
title = {Une caractérisation de la correspondance de {L}anglands locale pour {${\rm GL}(n)$}},
journal = {Bull. Soc. Math. France},
fjournal = {Bulletin de la Société Mathématique de France},
volume = {130},
year = {2002},
number = {4},
pages = {587--602},
issn = {0037-9484},
coden = {BSMFAA},
mrclass = {22E50},
mrnumber = {1947454},
mrreviewer = {Jean-Francois Dat},
zblnumber = {1029.22023},
} -
[Har01] M. Harris and R. Taylor, The Geometry and Cohomology of some Simple Shimura Varieties, Princeton, NJ: Princeton Univ. Press, 2001, vol. 151.
@book{Har01, mrkey = {1876802},
author = {Harris, Michael and Taylor, Richard},
title = {The Geometry and Cohomology of some Simple {S}himura Varieties},
series = {Ann. of Math. Studies},
volume = {151},
note = {with an appendix by Vladimir G. Berkovich},
publisher = {Princeton Univ. Press},
address = {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},
} -
[Iwa66] N. Iwahori, "Generalized Tits system (Bruhat decompostition) on $p$-adic semisimple groups," in Algebraic Groups and Discontinuous Subgroups, Providence, RI: Amer. Math. Soc., 1966, pp. 71-83.
@incollection{Iwa66, mrkey = {0215858},
author = {Iwahori, Nagayoshi},
title = {Generalized {T}its system ({B}ruhat decompostition) on {$p$}-adic semisimple groups},
booktitle = {Algebraic {G}roups and {D}iscontinuous {S}ubgroups},
venue = {{P}roc. {S}ympos. {P}ure {M}ath., {B}oulder, {C}olo., 1965},
pages = {71--83},
publisher = {Amer. Math. Soc.},
address = {Providence, RI},
year = {1966},
mrclass = {14.50},
mrnumber = {0215858},
mrreviewer = {D. J. Winter},
zblnumber = {0199.06901},
} -
[Kot99] R. E. Kottwitz and D. Shelstad, Foundations of Twisted Endoscopy, Paris: Math. Soc. France, 1999, vol. 255.
@book{Kot99, mrkey = {1687096},
author = {Kottwitz, Robert E. and Shelstad, Diana},
title = {Foundations of Twisted Endoscopy},
series = {Astérisque},
PUBLISHER={Math. Soc. France},
ADDRESS={Paris},
volume = {255},
year = {1999},
pages = {vi+190},
issn = {0303-1179},
mrclass = {22E55 (11F70 11R34 22-02 22E50)},
mrnumber = {1687096},
mrreviewer = {Volker J. Heiermann},
zblnumber = {0958.22013},
} -
[Kim02]
H. H. Kim and F. Shahidi, "Functorial products for ${ GL}_2\times{ GL}_3$ and the symmetric cube for ${ GL}_2$," Ann. of Math., vol. 155, iss. 3, pp. 837-893, 2002.
@article{Kim02, mrkey = {1923967},
author = {Kim, Henry H. and Shahidi, Freydoon},
title = {Functorial products for {${\rm GL}\sb 2\times{\rm GL}\sb 3$} and the symmetric cube for {${\rm GL}\sb 2$}},
note = {with an appendix by Colin J. Bushnell and Guy Henniart},
journal = {Ann. of Math.},
fjournal = {Annals of Mathematics. Second Series},
volume = {155},
year = {2002},
number = {3},
pages = {837--893},
issn = {0003-486X},
coden = {ANMAAH},
mrclass = {11F70 (22E55)},
mrnumber = {1923967},
mrreviewer = {A. Raghuram},
doi = {10.2307/3062134},
zblnumber = {1040.11036},
} -
[Lab11] J. Labesse, "Changement de base CM et séries discrètes," in On the Stabilization of the Trace Formula, Somerville, MA: Int. Press, 2011, vol. 1, pp. 429-470.
@incollection{Lab11, KEY={Lab11b},
mrkey = {2856380},
author = {Labesse, Jean-P.},
title = {Changement de base {CM} et séries discrètes},
booktitle = {On the Stabilization of the Trace Formula},
series = {Stab. Trace Formula Shimura Var. Arith. Appl.},
volume = {1},
pages = {429--470},
publisher = {Int. Press},
address = {Somerville, MA},
year = {2011},
mrclass = {22E45},
mrnumber = {2856380},
zblnumber = {1255.11027},
} -
[Lab11a] J. -P. Labesse, "Les facteurs de transfert pour les groupes unitaires," in On the Stabilization of the Trace Formula, Somerville, MA: Int. Press, 2011, vol. 1, pp. 411-421.
@incollection{Lab11a, KEY={Lab11a},
mrkey = {2856378},
author = {Labesse, J.-P.},
title = {Les facteurs de transfert pour les groupes unitaires},
booktitle = {On the Stabilization of the Trace Formula},
series = {Stab. Trace Formula Shimura Var. Arith. Appl.},
volume = {1},
pages = {411--421},
publisher = {Int. Press},
address = {Somerville, MA},
year = {2011},
mrclass = {22E50 (22E45)},
mrnumber = {2856378},
zblnumber = {1255.11027},
} -
[Lan87]
R. P. Langlands and D. Shelstad, "On the definition of transfer factors," Math. Ann., vol. 278, iss. 1-4, pp. 219-271, 1987.
@article{Lan87, mrkey = {0909227},
author = {Langlands, R. P. and Shelstad, D.},
title = {On the definition of transfer factors},
journal = {Math. Ann.},
fjournal = {Mathematische Annalen},
volume = {278},
year = {1987},
number = {1-4},
pages = {219--271},
issn = {0025-5831},
coden = {MAANA},
mrclass = {11S37 (11F70 11F72 22E35 22E45 22E50)},
mrnumber = {0909227},
mrreviewer = {Ernst-Wilhelm Zink},
doi = {10.1007/BF01458070},
zblnumber = {0644.22005},
} -
[Lus89]
G. Lusztig, "Affine Hecke algebras and their graded version," J. Amer. Math. Soc., vol. 2, iss. 3, pp. 599-635, 1989.
@article{Lus89, mrkey = {0991016},
author = {Lusztig, George},
title = {Affine {H}ecke algebras and their graded version},
journal = {J. Amer. Math. Soc.},
fjournal = {Journal of the American Mathematical Society},
volume = {2},
year = {1989},
number = {3},
pages = {599--635},
issn = {0894-0347},
mrclass = {16A64 (20H15 22E50)},
mrnumber = {0991016},
mrreviewer = {Fran{ç}ois Digne},
doi = {10.2307/1990945},
zblnumber = {0715.22020},
} -
[Min11] A. M’inguez, "Unramified representations of unitary groups," in On the stabilization of the trace formula, Int. Press, Somerville, MA, 2011, vol. 1, pp. 389-422.
@incollection{Min11, mrkey = {2856377},
author = {M{\'ı}nguez, Alberto},
title = {Unramified representations of unitary groups},
booktitle = {On the stabilization of the trace formula},
series = {Stab. Trace Formula Shimura Var. Arith. Appl.},
volume = {1},
pages = {389--422},
publisher = {Int. Press, Somerville, MA},
year = {2011},
mrclass = {22E50},
mrnumber = {2856377},
zblnumber = {1255.11027},
} -
[recent]
C. Moeglin, "Paquets stables des séries discrètes accessibles par endoscopie tordue; leur paramètre de Langlands," in Automorphic Forms and Related Geometry: Assessing the Legacy of I. I. Piatetski-Shapiro, Providence, RI: Amer. Math. Soc., 2014, vol. 614, pp. 295-336.
@incollection{recent,
author = {M{\oe}glin, Colette},
title = {Paquets stables des séries discrètes accessibles par endoscopie tordue; leur paramètre de {L}anglands},
BOOKTITLE={Automorphic Forms and Related Geometry: Assessing the Legacy of I. I. Piatetski-Shapiro},
VENUE={Proceedings of the conference, Yale University, New Haven, CT, April 23--27, 2002},
PUBLISHER={Amer. Math. Soc.},
ADDRESS={Providence, RI},
SERIES={Contemp. Math.},
VOLUME={614},
PAGES={295--336},
YEAR={2014},
zblnumber = {06315737},
DOI = {10.1090/conm/614/12254},
} -
[Moe07]
C. Moeglin, "Classification et changement de base pour les séries discrètes des groupes unitaires $p$-adiques," Pacific J. Math., vol. 233, iss. 1, pp. 159-204, 2007.
@article{Moe07, mrkey = {2366373},
author = {M{\oe}glin, Colette},
title = {Classification et changement de base pour les séries discrètes des groupes unitaires {$p$}-adiques},
journal = {Pacific J. Math.},
fjournal = {Pacific Journal of Mathematics},
volume = {233},
year = {2007},
number = {1},
pages = {159--204},
issn = {0030-8730},
coden = {PJMAAI},
mrclass = {22E50},
mrnumber = {2366373},
mrreviewer = {Joshua M. Lansky},
doi = {10.2140/pjm.2007.233.159},
zblnumber = {1157.22010},
} -
[Mok12] C. P. Mok, Endoscopic classification of representations of quasi-split unitary groups.
@misc{Mok12,
author = {Mok, Chung Pang},
title = {Endoscopic classification of representations of quasi-split unitary groups},
note = {to appear in \emph{Memoirs of the AMS}},
ARXIV= {1206.0882},
} -
[Mor99]
L. Morris, "Level zero $\bf G$-types," Compositio Math., vol. 118, iss. 2, pp. 135-157, 1999.
@article{Mor99, mrkey = {1713308},
author = {Morris, Lawrence},
title = {Level zero {$\bf G$}-types},
journal = {Compositio Math.},
fjournal = {Compositio Mathematica},
volume = {118},
year = {1999},
number = {2},
pages = {135--157},
issn = {0010-437X},
coden = {CMPMAF},
mrclass = {22E50},
mrnumber = {1713308},
mrreviewer = {Goran Mui{ć}},
doi = {10.1023/A:1001019027614},
zblnumber = {0937.22011},
} -
[Ngo10]
B. C. Ngô, "Le lemme fondamental pour les algèbres de Lie," Publ. Math. Inst. Hautes Études Sci., vol. 111, pp. 1-169, 2010.
@article{Ngo10, mrkey = {2653248},
author = {Ng{ô},
Bao Ch{â}u},
title = {Le lemme fondamental pour les algèbres de {L}ie},
journal = {Publ. Math. Inst. Hautes Études Sci.},
fjournal = {Publications Mathématiques. Institut de Hautes Études Scientifiques},
VOLUME = {111},
year = {2010},
pages = {1--169},
issn = {0073-8301},
mrclass = {22E35 (11S37 14D23 14G35 22E50)},
mrnumber = {2653248},
mrreviewer = {R. P. Langlands},
doi = {10.1007/s10240-010-0026-7},
zblnumber = {1200.22011},
} -
[Ree97]
M. Reeder, "Nonstandard intertwining operators and the structure of unramified principal series representations," Forum Math., vol. 9, iss. 4, pp. 457-516, 1997.
@article{Ree97, mrkey = {1457135},
author = {Reeder, Mark},
title = {Nonstandard intertwining operators and the structure of unramified principal series representations},
journal = {Forum Math.},
fjournal = {Forum Mathematicum},
volume = {9},
year = {1997},
number = {4},
pages = {457--516},
issn = {0933-7741},
coden = {FOMAEF},
mrclass = {22E50 (22E55)},
mrnumber = {1457135},
mrreviewer = {David Goldberg},
doi = {10.1515/form.1997.9.457},
zblnumber = {0882.22020},
} -
[Ree00]
M. Reeder, "Matrices for affine Hecke modules," J. Algebra, vol. 231, iss. 2, pp. 758-785, 2000.
@article{Ree00, mrkey = {1778170},
author = {Reeder, Mark},
title = {Matrices for affine {H}ecke modules},
journal = {J. Algebra},
fjournal = {Journal of Algebra},
volume = {231},
year = {2000},
number = {2},
pages = {758--785},
issn = {0021-8693},
coden = {JALGA4},
mrclass = {20C08},
mrnumber = {1778170},
mrreviewer = {Godofredo Iommi Amun{á}tegui},
doi = {10.1006/jabr.1999.8369},
zblnumber = {0979.20008},
} -
[Rib84] K. A. Ribet, "Congruence relations between modular forms," in Proceedings of the International Congress of Mathematicians, Vol. 1, 2, Warsaw, 1984, pp. 503-514.
@inproceedings{Rib84, mrkey = {0804706},
author = {Ribet, Kenneth A.},
title = {Congruence relations between modular forms},
booktitle = {Proceedings of the {I}nternational {C}ongress of {M}athematicians, {V}ol. 1, 2},
venue = {{W}arsaw, 1983},
pages = {503--514},
publisher = {PWN},
address = {Warsaw},
year = {1984},
mrclass = {11F33 (11G18)},
mrnumber = {0804706},
mrreviewer = {Yasutaka Ihara},
zblnumber = {0575.10024},
} -
[Rog90] J. D. Rogawski, Automorphic Representations of Unitary Groups in Three Variables, Princeton, NJ: Princeton Univ. Press, 1990, vol. 123.
@book{Rog90, mrkey = {1081540},
author = {Rogawski, Jonathan D.},
title = {Automorphic Representations of Unitary Groups in Three Variables},
series = {Ann. of Math. Studies},
volume = {123},
publisher = {Princeton Univ. Press},
address = {Princeton, NJ},
year = {1990},
pages = {xii+259},
isbn = {0-691-08586-2; 0-691-08587-0},
mrclass = {22E55 (11F70 11R39 22-02)},
mrnumber = {1081540},
mrreviewer = {David Joyner},
zblnumber = {0724.11031},
} -
[Suz82] M. Suzuki, Group Theory. I, New York: Springer-Verlag, 1982, vol. 247.
@book{Suz82, mrkey = {0648772},
author = {Suzuki, Michio},
title = {Group Theory. {I}},
series = {Grundl. Math. Wissen.},
volume = {247},
note = {translated from the Japanese by the author},
publisher = {Springer-Verlag},
year = {1982},
pages = {xiv+434},
isbn = {3-540-10915-3},
mrclass = {20-01},
mrnumber = {0648772},
mrreviewer = {B. Chang},
address = {New York},
zblnumber = {0472.20001},
} -
[Tat79] J. Tate, "Number theoretic background," in Automorphic Forms, Representations and $L$-Functions, Providence, RI: Amer. Math. Soc., 1979, vol. XXXIII, pp. 3-26.
@incollection{Tat79, mrkey = {0546607},
author = {Tate, J.},
title = {Number theoretic background},
booktitle = {Automorphic Forms, Representations and {$L$}-Functions},
venue = {{P}roc. {S}ympos. {P}ure {M}ath., {O}regon {S}tate {U}niv., {C}orvallis, {O}re., 1977, {P}art 2},
series = {Proc. Sympos. Pure Math.},
volume = {XXXIII},
pages = {3--26},
publisher = {Amer. Math. Soc.},
address = {Providence, RI},
year = {1979},
mrclass = {12A67},
mrnumber = {0546607},
mrreviewer = {A. I. Vinogradov},
zblnumber = {0422.12007},
} -
[Tay89]
R. Taylor, "On Galois representations associated to Hilbert modular forms," Invent. Math., vol. 98, iss. 2, pp. 265-280, 1989.
@article{Tay89, mrkey = {1016264},
author = {Taylor, Richard},
title = {On {G}alois representations associated to {H}ilbert modular forms},
journal = {Invent. Math.},
fjournal = {Inventiones Mathematicae},
volume = {98},
year = {1989},
number = {2},
pages = {265--280},
issn = {0020-9910},
coden = {INVMBH},
mrclass = {11R39 (11F12 11F33 11F41 11G18)},
mrnumber = {1016264},
mrreviewer = {Bas Edixhoven},
doi = {10.1007/BF01388853},
zblnumber = {0705.11031},
} -
@misc{Tho12, KEY={Tho14},
author = {Thorne, Jack A.},
title = {Automorphy lifting for residually reducible $l$-adic {G}alois representations},
SORTYEAR={2014},
note = {{\it J. Amer. Math. Soc.},
electronically published on June 6, 2014},
DOI = {10.1090/S0894-0347-2014-00812-2},
} -
[Tho10]
J. Thorne, "On the automorphy of $l$-adic Galois representations with small residual image," J. Inst. Math. Jussieu, vol. 11, iss. 4, pp. 855-920, 2012.
@article{Tho10, mrkey = {2979825},
author = {Thorne, Jack},
title = {On the automorphy of {$l$}-adic {G}alois representations with small residual image},
note = {with an appendix by Robert Guralnick, Florian Herzig, Richard Taylor and Thorne},
journal = {J. Inst. Math. Jussieu},
fjournal = {Journal of the Institute of Mathematics of Jussieu. JIMJ. Journal de l'Institut de Mathématiques de Jussieu},
volume = {11},
year = {2012},
number = {4},
pages = {855--920},
issn = {1474-7480},
mrclass = {11F80 (11R34)},
mrnumber = {2979825},
mrreviewer = {Fausto Jarqu{\'ı}n Z{á}rate},
doi = {10.1017/S1474748012000023},
zblnumber = {1269.11054},
} -
[Tit79] J. Tits, "Reductive groups over local fields," in Automorphic Forms, Representations and $L$-Functions, Providence, RI: Amer. Math. Soc., 1979, vol. XXXIII, pp. 29-69.
@incollection{Tit79, mrkey = {0546588},
author = {Tits, J.},
title = {Reductive groups over local fields},
booktitle = {Automorphic Forms, Representations and {$L$}-Functions},
venue = {{P}roc. {S}ympos. {P}ure {M}ath., {O}regon {S}tate {U}niv., {C}orvallis, {O}re., 1977, {P}art 1},
series = {Proc. Sympos. Pure Math.},
volume = {XXXIII},
pages = {29--69},
publisher = {Amer. Math. Soc.},
address = {Providence, RI},
year = {1979},
mrclass = {20G25 (20G10)},
mrnumber = {0546588},
zblnumber = {0415.20035},
} -
[Wal13] J. -L. Waldspurger, Stabilisation de la formule des traces tordue I: endoscopie tordue sur un corps local.
@misc{Wal13,
author = {Waldspurger, J.-L.},
title = {Stabilisation de la formule des traces tordue {I}: endoscopie tordue sur un corps local},
arxiv = {1401.4569},
} -
[Wal13a] J. -L. Waldspurger, Stabilisation de la formule des traces tordue II: intégrales orbitales et endoscopie sur un corps local non-archimédien; définitions et énoncés des résultats.
@misc{Wal13a,
author = {Waldspurger, J.-L.},
TITLE = {Stabilisation de la formule des traces tordue {II}: intégrales orbitales et endoscopie sur un corps local non-archimédien; définitions et énoncés des résultats},
ARXIV={1401.7127},
} -
[Wal97]
J. -L. Waldspurger, "Le lemme fondamental implique le transfert," Compositio Math., vol. 105, iss. 2, pp. 153-236, 1997.
@article{Wal97, mrkey = {1440722},
author = {Waldspurger, J.-L.},
title = {Le lemme fondamental implique le transfert},
journal = {Compositio Math.},
fjournal = {Compositio Mathematica},
volume = {105},
year = {1997},
number = {2},
pages = {153--236},
issn = {0010-437X},
mrclass = {22E50 (11F72 11F85 22E35)},
mrnumber = {1440722},
mrreviewer = {David Manderscheid},
doi = {10.1023/A:1000103112268},
zblnumber = {0871.22005},
} -
[Wal09]
J. -L. Waldspurger, "À propos du lemme fondamental pondéré tordu," Math. Ann., vol. 343, iss. 1, pp. 103-174, 2009.
@article{Wal09, mrkey = {2448443},
author = {Waldspurger, J.-L.},
title = {À propos du lemme fondamental pondéré tordu},
journal = {Math. Ann.},
fjournal = {Mathematische Annalen},
volume = {343},
year = {2009},
number = {1},
pages = {103--174},
issn = {0025-5831},
coden = {MAANA},
mrclass = {22E35 (11F72 22E50)},
mrnumber = {2448443},
mrreviewer = {Anne-Marie H. Aubert},
doi = {10.1007/s00208-008-0267-7},
zblnumber = {1158.22011},
} -
[Wal09a]
J. Waldspurger, "Endoscopie et changement de caractéristique: intégrales orbitales pondérées," Ann. Inst. Fourier $($Grenoble$)$, vol. 59, iss. 5, pp. 1753-1818, 2009.
@article{Wal09a, mrkey = {2573190},
author = {Waldspurger, Jean-Loup},
title = {Endoscopie et changement de caractéristique: intégrales orbitales pondérées},
journal = {Ann. Inst. Fourier $($Grenoble$)$},
fjournal = {Université de Grenoble. Annales de l'Institut Fourier},
volume = {59},
year = {2009},
number = {5},
pages = {1753--1818},
issn = {0373-0956},
coden = {AIFUA7},
mrclass = {22E35 (22E50)},
mrnumber = {2573190},
mrreviewer = {Anne-Marie H. Aubert},
zblnumber = {1184.22003},
doi = {10.5802/aif.2476},
}