Work

Hodge Cycles and Quadratic Relations Between Holomorphic Periods on Cm Abelian Varieties

Year: 2025

Type: article

Abstract: In this paper, we prove the following result advocating the importance of monomial quadratic relations between holomorphic CM periods. For any simple CM abelian variety A , we can construct a CM abelian variety B such that all non-trivial Hodge relations between the holomorphic periods of the product $A\times B$ are generated by monomial quadratic ones which are also explicit. Moreover, B splits over the Galois closure of the CM field associated with A .

Source: Journal of the Institute of Mathematics of Jussieu

DOI: 10.1017/s1474748025101291

Authors: Ziyang Gao, Emmanuel Ullmo

Institutions: University of California, Los Angeles, Université Paris-Saclay

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

OpenAlex ID: W4414361838