Jul 11 – 29, 2022
IHES
Europe/Paris timezone

Cohomology Sheaves of Stacks of Shtukas (1/2)

Jul 19, 2022, 3:00 PM
1h
Marilyn and James Simons Conference Center (IHES)

Marilyn and James Simons Conference Center

IHES

35 route de Chartres, F-91440 Bures-sur-Yvette, France

Speaker

Prof. Cong XUE (IMJ-PRG)

Description

Cohomology sheaves and cohomology groups of stacks of shtukas are used in the Langlands program for function fields. We will explain (1) how the Eichler-Shimura relations imply the finiteness property of the cohomology groups, (2) how the finiteness and Drinfeld's lemma imply the action of the Weil group of the function field on the cohomology groups, and (3) how this action and the "Zorro lemma" imply the smoothness of the cohomology sheaves. The smoothness will be used in Sam Raskin’s lecture.

Presentation materials