A “strange” functional equation for Eisenstein series and miraculous duality on the moduli stack of bundles
[Une équation fonctionnelle “étrange” pour les séries d'Eisenstein et la dualité miraculeuse sur le champ des modules des fibrés]
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 50 (2017) no. 5, pp. 1123-1162.

Dans cet article, on démontre que la dualité de Verdier habituelle ne tenant pas pour le champ BunG, on peut la remplacer par un autre foncteur de dualité. On étudie la relation entre celui-ci et le foncteur de série d'Eisenstein.

We show that the failure of the usual Verdier duality on BunG leads to a new duality functor on the category of D-modules, and we study its relation to the operation of Eisenstein series.

DOI : 10.24033/asens.2641
Classification : 14F05, 14H60
Keywords: Moduli stack of bundles, Verdier duality, Eisenstein series.
Mot clés : Le champ des modules des fibrés, dualité de Verdier, série d'Eisenstein. 
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     author = {Gaitsgory, Dennis},
     title = {A {\textquotedblleft}strange{\textquotedblright} functional equation  for {Eisenstein} series  and miraculous duality  on the moduli stack of bundles},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {1123--1162},
     publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
     volume = {Ser. 4, 50},
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     doi = {10.24033/asens.2641},
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Gaitsgory, Dennis. A “strange” functional equation  for Eisenstein series  and miraculous duality  on the moduli stack of bundles. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 50 (2017) no. 5, pp. 1123-1162. doi : 10.24033/asens.2641. http://www.numdam.org/articles/10.24033/asens.2641/

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