Deformation of $\ell$-adic sheaves with Undeformed Local Monodromy

Abstract

Let $X$ be a smooth connected algebraic curve over an algebraically closed field $k$. We study the deformation of $\ell$-adic Galois representations of the function field of $X$ while keeping the local Galois representations at all places undeformed.

21 pages. To appear in Journal of Number Theory