Companions on Artin stacks
Algebraic Geometry
2019-06-24 v7 Number Theory
Abstract
Deligne's conjecture that -adic sheaves on normal schemes over a finite field admit -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.
Cite
@article{arxiv.1512.08929,
title = {Companions on Artin stacks},
author = {Weizhe Zheng},
journal= {arXiv preprint arXiv:1512.08929},
year = {2019}
}
Comments
26 pages. v7: fixed typos, to appear in Math. Z