Cubic fourfolds, Kuznetsov components, and Chow motives
Lie Fu
IRMA, Université de Strasbourg, FranceCharles Vial
Universität Bielefeld, Germany
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Abstract
We prove that the Chow motives of two smooth cubic fourfolds whose Kuznetsov components are Fourier–Mukai equivalent are isomorphic as Frobenius algebra objects. As a corollary, there exists a Galois-equivariant isomorphism between their -adic cohomology Frobenius algebras. We also discuss the case where the Kuznetsov component of a smooth cubic fourfold is equivalent to the derived category of a K3 surface.
Cite this article
Lie Fu, Charles Vial, Cubic fourfolds, Kuznetsov components, and Chow motives. Doc. Math. 28 (2023), no. 4, pp. 827–856
DOI 10.4171/DM/925