Title: Arithmetic Representations of Fundamental Groups
Speaker: Daniel Litt (Columbia University)
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 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 $p^N$.
Seminar URL: https://research.math.osu.edu/agseminar/