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.

References in corpus (1)

• Cycles on Shimura varieties via geometric Satake

Cited by in corpus (4)

• Geometrization of the local Langlands correspondence
• Coherent sheaves on the stack of Langlands parameters
• Automorphic functions as the trace of Frobenius
• The plectic conjecture over function fields