Companions on Artin stacks

Abstract

Deligne's conjecture that $\ell$-adic sheaves on normal schemes over a finite field admit ${\ell }^{\prime }$-companions was proved by L. Lafforgue in the case of curves and by Drinfeld in the case of smooth schemes. In this paper, we extend Drinfeld's theorem to smooth Artin stacks and deduce Deligne's conjecture for coarse moduli spaces of smooth Artin stacks. We also extend related theorems on Frobenius eigenvalues and traces to Artin stacks.

26 pages. v7: fixed typos, to appear in Math. Z

References in corpus (4)

• A finiteness theorem for Galois representations of function fields over finite fields (after Deligne)
• Independence of l in Lafforgue's theorem
• Théorème de Gabber d'indépendance de $l$
• Independence of $\ell$ for the supports in the Decomposition Theorem

Cited by in corpus (1)

• Compatible systems and ramification