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# Jeff Achter : Monodromy in Families of Abelian Varieties

The p-power torsion of a family of elliptic curves in characteristic p defines a local system on the base space. Igusa shows that the associated monodromy representation is maximal, in the sense that the image of the fundamental group is the full automorphism group of a fiber. I will discuss variants of this situation which can make the group in question bigger (higher-dimensional abelian varieties), smaller (with large endomorphism rings), or simply different (and no physical p-torsion). I hope to interpret these results as statements about certain differential equations.

**Category**: Other Meetings and Events**Duration**: 01:05:39**Date**: December 7, 1999 at 4:00 PM**Views**: 34-
**Tags:**seminar, Geometry/Topology Seminar

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