Existence of compatible systems of lisse sheaves on arithmetic schemes
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Publication:506176
DOI10.2140/ANT.2017.11.181zbMATH Open1361.11045arXiv1509.05941OpenAlexW2197757627MaRDI QIDQ506176
Publication date: 31 January 2017
Published in: Algebra \& Number Theory (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/1509.05941
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