Weizhe Zheng
Published 2015-12-30Version 1
Deligne's conjecture that $\ell$-adic sheaves on normal schemes over a finite field admit $\ell'$-companions was proved by 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 to their coarse moduli spaces. In contrast to the case of smooth schemes, our proof relies on Gabber's theorem on the preservation of companionship.
Hyperbolicity of coarse moduli spaces and isotriviality for certain families
Singularities appearing on generic fibers of morphisms between smooth schemes
The moduli spaces of hyperelliptic curves and binary forms
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