Arithmetic Restrictions on Geometric Monodromy

2016/07/19 by Daniel Litt, Litt, Daniel
Mathematics · #Algebraic Geometry and Number Theory #Advanced Topics in Algebra #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1607.05740

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.

Citations

• Good Reduction of Abelian Varieties

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