Abstract
Dans cet article, on étudie la cohomologie de la fibration de Hitchin tronquée introduite dans un article précédent. On étend les principaux théorèmes de Ngô sur la cohomologie de la partie elliptique de la fibration de Hitchin. Comme conséquence, on obtient une démonstration du lemme fondamental pondéré d’Arthur.
In this paper, we study the cohomology of the truncated Hitchin fibration, which was introduced in a previous paper. We extend Ngô’s main theorems on the cohomology of the elliptic part of the Hitchin fibration. As a consequence, we get a proof of Arthur’s weighted fundamental lemma.
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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},
CODEN = {CMPMAF},
MRCLASS = {22E50 (11F72 11F85 22E35)},
MRNUMBER = {1440722},
MRREVIEWER = {David Manderscheid},
DOI = {10.1023/A:1000103112268},
ZBLNUMBER = {0871.22005},
} -
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@article {Wlfp1, 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},
} -
[Wlfp2] J. Waldspurger, "Endoscopie et changement de caractéristique: intégrales orbitales pondérées," Ann. Inst. Fourier $($Grenoble$)$, vol. 59, iss. 5, pp. 1753-1818, 2009.
@article {Wlfp2, 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},
DOI = {10.5802/aif.2476},
ZBLNUMBER = {1184.22003},
} -
[Whitehouse] D. Whitehouse, "The twisted weighted fundamental lemma for the transfer of automorphic forms from $ GSp(4)$," in Formes Automorphes. II. Le cas du Groupe ${{G}}{S}p(4)$, Paris: Soc. Math. France, 2005, vol. 302, pp. 291-436.
@incollection{Whitehouse, MRKEY = {2234863},
AUTHOR = {Whitehouse, David},
TITLE = {The twisted weighted fundamental lemma for the transfer of automorphic forms from {$\rm GSp(4)$}},
BOOKTITLE = {Formes Automorphes. II. Le cas du Groupe ${\rm{G}}{S}p(4)$},
JOURNAL = {Astérisque},
FJOURNAL = {Astérisque},
VOLUME = {302},
PUBLISHER = {Soc. Math. France},
ADDRESS = {Paris},
YEAR = {2005},
PAGES = {291--436},
ISSN = {0303-1179},
MRCLASS = {11F70 (11F72 11R39 22E35)},
MRNUMBER = {2234863},
MRREVIEWER = {Mahdi Asgari},
ZBLNUMBER = {1097.11025},
}
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