Department of Mathematics,
University of California San Diego

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Thesis Defense

Jack J Garzella
UC San Diego

P-adic geometry of finite and infinite type

Abstract:

We present four results: in the first, we give a fast algorithms for calculating
the quasi-F-split height of Calabi-Yau hypersurfaces in characteristic p. In the second, we give a fast algorithm for calculating the zeta functions of projective hypersurfaces in characteristic p. In the third, we show that Berkovich’s affinoid algebras and dagger algebras are F-instersection flat (and thus contain big test elements). In the fourth, we consider the problem of the nullstellensatz of perfectoid Tate algebras. 

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