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arXiv · 2009.13173

Cubic fourfolds, Kuznetsov components and Chow motives

Lie Fu·Charles Vial
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Abstract

We prove that the Chow motives of two smooth cubic fourfolds whose Kuznetsov components are Fourier-Mukai derived-equivalent are isomorphic as Frobenius algebra objects. As a corollary, we obtain that there exists a Galois-equivariant isomorphism between their l-adic cohomology Frobenius algebras. We also discuss the case where the Kuznetsov component of a smooth cubic fourfold is Fourier-Mukai derived-equivalent to a K3 surface.

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Lie Fu, Charles Vial. 2020-09-28. Cubic fourfolds, Kuznetsov components and Chow motives. https://doi.org/10.4171/dm/925

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