A FINITENESS THEOREM FOR GALOIS REPRESENTATIONS OF FUNCTION FIELDS OVER FINITE FIELDS (AFTER DELIGNE)

By H. Esnault, M. Kerz. 2012

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We give a detailed account of Deligne's letter (13) to Drinfeld dated June 18, 2011, in which he shows that there are nitely many irreducible lisse Q'-sheaves with bounded ramica- tion, up to isomorphism and up to twist, on a smooth variety dened over a nite eld. The proof relies on Laorgue's Lang- lands correspondence over curves (27). In addition, Deligne shows the existence of ane

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

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