|Title: Arithmetic Restrictions on Geometric Monodromy|
|Speaker: Daniel Litt of Columbia University|
|Contact: David Zureick-Brown, firstname.lastname@example.org|
|Date: 2016-08-30 at 4:00PM|
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 Gal(k/k) on pi_1(X), where k is a finite or p-adic field. As a sample application of our techniques, we show that if A is a non-constant Abelian variety over C(t), such that A[l] is split for some odd prime l, then A has at least four points of bad reduction.
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