Two results on the Hodge structure of complex tori

2021/06/21 by François Charles, Charles, François
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2106.11069

openalex publication_date 2021/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Mixed Hodge Structures
• A generalization of the Kuga-Satake construction
• The cohomology of a variation of polarized Hodge structures over a quasi-compact Kähler manifold
• Kuga-Satake varieties and the Hodge conjecture
• Categories of complex variations of Hodge structure over compact K"ahler manifolds