Existence of compatible systems of lisse sheaves on arithmetic schemes

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.

Some arguments are simplified and corrected. Typos are fixed. To appear in Algebra and Number Theory

References in corpus (1)

• Rigidity and a Riemann-Hilbert correspondence for p-adic local systems