Cong Xue - Cohomology of stacks of shtukas
Channel: Institut des Hautes Études Scientifiques (IHÉS)
Date: 08/06/2021

Correction: The affiliation of Lei Fu is Tsinghua University.

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.