Integral Chow motives of derived equivalent K3 surfacesSeminar Algebraic Geometry (SAG)

by Evgeny Shinder (Sheffield)

Thursday Jul 23, 2026, 10:30 AM → 11:30 AM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

We prove that if X, Y are derived equivalent complex K3 surfaces, then the integral Chow motives are typically not isomorphic, but are always stably isomorphic. This unfies the result of Huybrechts for isomorphism of rational Chow motives with the result of Mukai for the stable equivalence of integral Hodge structures. Under some mild assumptions, the same result holds for K3 surfaces over nonclosed fields of characteristic zero. For the proofs we rely on known results about zero-cycles on K3 surfaces and set up the machinery of Tate-stable equivalence for integral Chow motives. This is a joint work in progress with Hsueh-Yung Lin and Pavel Sechin.