Conference on Arithmetic Geometry in honor of Luc Illusie

Collection Conference on Arithmetic Geometry in honor of Luc Illusie

Organizer(s) Lei Fu (Tsinghua University), Fabrice Orogozo (CNRS&IMJ-PRG), Weizhe Zheng (MCM, AMSS, CAS)
Date(s) 07/06/2021 - 11/06/2021
00:00:00 / 00:00:00
2 22

Cohomology of stacks of shtukas

By Cong Xue

Let X be a geometrically connected smooth projective curve over Fq and G a reductive group over the function field of X. For any finite set I we have the stacks of shtukas over X^I, and the Satake sheaves over the stacks of shtukas.

Let N be a level structure. We prove that the relative cohomology sheaf of the stack of shtukas is ind-smooth over (X - N)^I. Moreover, we hope to prove that the cohomology of the special fiber of the stack of shtukas at a point in the level with coefficients in the nearby cycles is isomorphic to the cohomology of the generic fiber of the stack of shtukas.

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