Taylor Dupuy, University of Vermont
11:30 AM - 12:30 PM
Kodaira-Spencer classes classify local deformations of schemes. In this talk we construct cohomology classes associated to smooth schemes over p-adic rings which behave like Kodaira-Spencer classes. These cohomology classes are obstructions to lifts of the Frobenius modulo p^2. We will explain how to construct these classes, explain how these classes behave under morphisms of varieties, and relate them to a problem of Coleman’s concerning the non-existence of non-hyperelliptic CM Jacobians for large genus (Coleman’s original conjecture was false). Whether or not Jacobians have CM turns out to be determined by the behavior of a “wittfinitesimal Torelli map”. In the Kodaira-Spencer setting this map is called the “infinitesimal Torelli map” and is known to be injective outside the hyperelliptic locus (in characteristic zero).
Event contact: dinesh dot thakur at rochester dot edu