On finiteness of twisted forms of hyperkähler varieties

Abstract: For a finite field extension $L/K$ and a variety $X$ over $K$, let $Tw_{L/K} (X)$ be the set of isomorphism classes of varieties $Y$ over $K$ which are isomorphic to $X$ after the base change to $L$ (i.e. the set of twisted forms of $X$ via $L/K$). In this talk, we prove the finiteness of $Tw_{L/K}$ for K3 surfaces of characteristic away from 2 and hyperkähler varieties of characteristic 0. This work is a generalization of Cattaneo-Fu's work on real forms of hyperkähler varieties. We also give an application to the finiteness of derived equivalent twisted forms of hyperkähler varieties.

number theory

Audience: researchers in the discipline

POINT: New Developments in Number Theory

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