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arXiv · 1509.05941

Existence of compatible systems of lisse sheaves on arithmetic schemes

Koji Shimizu
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Abstract

Deligne conjectured that a single l-adic lisse sheaf on a normal variety over a finite field can be embedded into a compatible system of l'-adic lisse sheaves with various l'. 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 Z and prove some cases using Lafforgue's result and the work of Barnet-Lamb, Gee, Geraghty, and Taylor.

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Koji Shimizu. 2016-11-23. Existence of compatible systems of lisse sheaves on arithmetic schemes. https://doi.org/10.2140/ant.2017.11.181

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