## Algebraic Geometry Seminar

Daniel Litt

Columbia

Arithmetic restrictions on geometric monodromy

**Abstract:**Let X be an algebraic variety over a field k. Which representations of pi_1(X) arise from geometry, e.g. as monodromy representations on the cohomology of a family of varieties over X? We study this question by analyzing the action of the Galois group of k on the fundamental group of X. As a sample application of our techniques, we show that if X is a smooth variety over a field of characteristic zero, and p is a prime, then there exists an integer N=N(X,p) satisfying the following: any irreducible p-adic representation of the fundamental group of X which arises from geometry is non-trivial mod p^N.

Wednesday November 30, 2016 at 1:00 PM in SEO 427