Motives of isogenous K3 surfaces

Abstract

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.