2017/05/11 by Daniel Huybrechts, Huybrechts, Daniel
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.1705.04063
12 pages. Final version. To appear in Commentarii Mathematici Helvetici. In view of Efimov's recent counterexample, the conjecture is not making any assertion anymore about equality in (localizations of) the Grothendieck ring of varieties. Formulation and proof of Theorem 1.1 have been corrected
arxiv created 2018/03/14 · arxiv updated 2018/03/15
We prove that isogenous K3 surfaces have isomorphic Chow motives. This provides a motivic interpretation of a long standing conjecture of Safarevich which has been settled only recently by Buskin. The main step consists of a new proof of Safarevich's conjecture that circumvents the analytic parts in Buskin's approach, avoiding twistor spaces and non-algebraic K3 surfaces.