On a Conjecture of Deligne

By V. Drinfeld. 2010

88 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c26a9da1c100ce7271eec67c94d08336d8ca9f16

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In Computational Theory and Mathematics

1. M. Kerz
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In Geometry and Topology

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In Mathematical Physics

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Citations in the corpus

• A FINITENESS THEOREM FOR GALOIS REPRESENTATIONS OF FUNCTION FIELDS OVER FINITE FIELDS (AFTER DELIGNE) (2012, methodology): “Acknowledgment: Our note gives an account of the 9 dense pages written by Deligne to Drinfeld [13].”