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arXiv · 1007.4004

On a conjecture of Deligne

Vladimir Drinfeld
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Abstract

Let X be a smooth variety over $F_p$. Let E be a number field. For each nonarchimedean place $\lambda$ of E prime to p consider the set of isomorphism classes of irreducible lisse $\bar{E}_{\lambda}$-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 $\lambda$. 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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Vladimir Drinfeld. 2010-07-22. On a conjecture of Deligne. https://arxiv.org/abs/1007.4004

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