Smoothness of cohomology sheaves of stacks of shtukas

Abstract

We prove, for all reductive groups, that the cohomology sheaves with compact support of stacks of shtukas are ind-smooth over $(X - N)^I$ and that their geometric generic fibers are equiped with an action of $\text{Weil}(X - N, \overline{\eta})^I$. Our method does not use any compactification of stacks of shtukas.