# Algebraic Geometry Seminar

#### Arithmetic restrictions on geometric monodromy

**Speaker:**
Daniel Litt, Columbia University

**Location:**
Warren Weaver Hall 317

**Date:**
Tuesday, November 7, 2017, 3:30 p.m.

**Synopsis:**

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 normal 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, non-trivial p-adic representation of the fundamental group of X, which arises from geometry, is non-trivial mod p^N.