Arithmetic Restrictions on Geometric Monodromy
Algebraic Geometry
2016-12-22 v2 Number Theory
Representation Theory
Abstract
Let X be a normal complex algebraic variety, and p a prime. We show that there exists an integer N=N(X, p) such that: any non-trivial, irreducible representation of the fundamental group of X, which arises from geometry, must be non-trivial mod p^N. The proof involves an analysis of the action of the Galois group of a finitely generated field on the etale fundamental group of X. We also prove many arithmetic statements about fundamental groups which are of independent interest, and give several applications.
Cite
@article{arxiv.1607.05740,
title = {Arithmetic Restrictions on Geometric Monodromy},
author = {Daniel Litt},
journal= {arXiv preprint arXiv:1607.05740},
year = {2016}
}
Comments
57 pages, 1 figure. Dramatic improvements to main results. Significant improvements to exposition, several new examples, and major reorganization. Basically completely rewritten. Comments welcome!