Existence of compatible systems of lisse sheaves on arithmetic schemes
Number Theory
2017-02-01 v2
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.
Keywords
Cite
@article{arxiv.1509.05941,
title = {Existence of compatible systems of lisse sheaves on arithmetic schemes},
author = {Koji Shimizu},
journal= {arXiv preprint arXiv:1509.05941},
year = {2017}
}
Comments
Some arguments are simplified and corrected. Typos are fixed. To appear in Algebra and Number Theory