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.