Geometry/Topology Seminar
Tuesday, December 7, 1999, 4:00pm, 120 Physics
Jeff Achter
Monodromy in Families of Abelian Varieties
Abstract:- 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.
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