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Commentarii Mathematici Helvetici

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Volume 94, Issue 3, 2019, pp. 445–458
DOI: 10.4171/CMH/465

Published online: 2019-09-25

Motives of isogenous K3 surfaces

Daniel Huybrechts[1]

(1) Universität Bonn, Germany

We prove that isogenous K3 surfaces have isomorphic Chow motives. This provides a motivic interpretation of a long standing conjecture of Šafarevic which has been settled only recently by Buskin. The main step consists of a new proof of Šafarevic’s conjecture that circumvents the analytic parts in [2], avoiding twistor spaces and non-algebraic K3 surfaces.

Keywords: K3 surfaces, derived categories, motives, Hodge conjecture, Brauer groups, twisted K3 surfaces

Huybrechts Daniel: Motives of isogenous K3 surfaces. Comment. Math. Helv. 94 (2019), 445-458. doi: 10.4171/CMH/465