Algebraic Geometry Seminar - Daniel Litt

October 18, 2017
Tuesday, November 14, 2017 - 3:00pm to 4:00pm
Math Tower 154
Daniel Litt

Title: Arithmetic Representations of Fundamental Groups

SpeakerDaniel 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 URLhttps://research.math.osu.edu/agseminar/

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