Two results on the Hodge structure of complex tori

摘要

We prove two results regarding Hodge structures appearing in the cohomology of complex tori. First, we prove that if a polarizable Hodge structure appears in the cohomology of a complex torus T, it appears in the cohomology of an abelian variety isomorphic to a subquotient of T. Second, we prove a universality result for the Kuga-Satake construction applied to Hodge structures of K3 type that might not be polarized.