Equivariant derived equivalence and rational points on K3 surfaces

Abstract

We study arithmetic properties of derived equivalent K3 surfaces over the field of Laurent power series, using the equivariant geometry of K3 surfaces with cyclic groups actions.

Involutions on K3 surfaces and derived equivalence

“…Derived equivalence also means that the lattices Pic(X 1 ) and Pic(X 2 ) belong to the same genus. Over nonclosed fields, or in equivariant contexts, derived equivalence is a subtle property, see, e.g., [HT17], [HT22].…”

“…Here we investigate involutions up to derived equivalence, i.e., derived equivalences respecting involutions. Our interest in "derived" phenomena was sparked by a result in [Sos10]-there exist complex conjugate, derived equivalent nonisomorphic K3 surfaces-as well as our investigations of arithmetic problems on K3 surfaces [HT17], [HT22].…”