On a conjecture of Deligne

2010/07/22 by Drinfeld, Vladimir · 2 citations
#11G35 #14G15 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1007.4004

Abstract

Let X be a smooth variety over F_p. Let E be a number field. For each nonarchimedean place λ of E prime to p consider the set of isomorphism classes of irreducible lisse E_λ-sheaves on X with determinant of finite order such that for every closed point x in X the characteristic polynomial of the Frobenius F_x has coefficents in E. We prove that this set does not depend on λ. The idea is to use a method developed by G.Wiesend to reduce the problem to the case where X is a curve. This case was treated by L. Lafforgue.

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• G-companions on algebraic stacks and applications to canonical ℓ-adic local systems on Shimura stacks
• Density of integral points in the Betti moduli of quasi-projective varieties

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