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.


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.