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Arithmetic of Kummer-type fourfolds

Sarah Frei (Dartmouth College)
Tuesday, April 4, 2023 - 1:45pm
PDL C-38
Title pre talk: Arithmetic and derived categories
Abstract talk: The derived category of coherent sheaves has proven to be a useful tool for studying the geometry of algebraic varieties. In this talk, I will discuss various ways in which the derived category does and doesn't capture the arithmetic of algebraic varieties. I will focus on the existence of rational points and cohomology as Galois representations. Along the way, I'll point out interesting open questions in this area. 
Title: Arithmetic of Kummer-type fourfolds Abstract: Projective hyperkahler varieties are one of the fundamental building blocks for compact Kahler varieties with trivial first Chern class. In many ways they can be thought of as higher-dimensional generalizations of K3 surfaces, and consequently we expect them to exhibit interesting arithmetic properties. In this talk, I will discuss generalized Kummer fourfolds, hyperkahler varieties which arise as moduli spaces of sheaves on an abelian surface. In joint work with Katrina Honigs, we characterize the Galois action on the even cohomology, which has natural consequences for derived equivalences between Kummer fourfolds.
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