Bi-$\overline{\mathbb{Q}}$-structures on Hermitian symmetric spaces and quadratic relations between CM periods
Abstract
In this paper, we introduce the notion of a bi- \overline{\mathbb{Q}} -structure on the tangent space at a CM point on a locally Hermitian symmetric domain. We prove that this bi- \overline{\mathbb{Q}} -structure decomposes into the direct sum of 1 -dimensional bi- \overline{\mathbb{Q}} -subspaces, and make this decomposition explicit for the moduli space of abelian varieties \mathbb{A}_{g} .We propose an analytic subspace conjecture , which is the analogue of the Wüstholz’s analytic subgroup theorem in this context. We show that this conjecture, applied to \mathbb{A}_{g} , implies that all quadratic \overline{\mathbb{Q}} -relations among the holomorphic periods of CM abelian varieties arise from elementary ones.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Geometry and complex manifolds
Publication details
- Journal / source
- Documenta Mathematica
- Volume
- 31
- Issue
- 4
- Pages
- 935–981
- Publication date
- 16 January 2026
- Language
- EN