The University of Arizona

Arithmetic representations of fundamental groups

Arithmetic representations of fundamental groups

Series: Algebraic Geometry Seminar
Location: ENR 2 S395
Presenter: Daniel Litt, Columbia University

Let X be an algebraic variety over a field k.  Which representations of π1(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, and prove several fundamental structural results about this action.

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) such that any non-trivial p-adic representation of the fundamental group of X, which arises from geometry, is non-trivial mod pN.

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