Vol. 11, No. 1, 2017

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Existence of compatible systems of lisse sheaves on arithmetic schemes

Koji Shimizu

Vol. 11 (2017), No. 1, 181–211

Deligne conjectured that a single -adic lisse sheaf on a normal variety over a finite field can be embedded into a compatible system of -adic lisse sheaves with various . Drinfeld used Lafforgue’s result as an input and proved this conjecture when the variety is smooth. We consider an analogous existence problem for a regular flat scheme over and prove some cases using Lafforgue’s result and the work of Barnet-Lamb, Gee, Geraghty, and Taylor.

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arithmetic geometry, lisse sheaves, compatible system
Mathematical Subject Classification 2010
Primary: 11G35
Secondary: 11F80
Received: 22 February 2016
Revised: 19 October 2016
Accepted: 17 November 2016
Published: 23 January 2017
Koji Shimizu
Department of Mathematics
Harvard University
Cambridge, MA 02138
United States