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Title:
Derived equivalent K3 surfaces and their motives as algebra objects.
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Abstract:
We show that two (twisted) derived K3 surfaces have isomorphic rational Chow motives as Frobenius algebra objects. Combined with Huybrechts' result, we get a motivic characterization for two K3 surfaces to be isogenous. We raise some questions for higher-dimensional hyper-Kähler varieties. In the non-commutative direction, we prove an analogous relation between the motives of two cubic fourfolds with equivalent Kuznetsov component. The talk is based on a series of joint work with Charles Vial.
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