Hodge cycles and quadratic relations between holomorphic periods on CM abelian varieties

Fuente: arXiv
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Main Authors: Gao, Ziyang, Ullmo, Emmanuel
Format: Preprint
Published: 2024
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_version_ 1866914266743832576
author Gao, Ziyang
Ullmo, Emmanuel
author_facet Gao, Ziyang
Ullmo, Emmanuel
contents 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 $A$.
format Preprint
id arxiv_https___arxiv_org_abs_2411_12249
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Hodge cycles and quadratic relations between holomorphic periods on CM abelian varieties
Gao, Ziyang
Ullmo, Emmanuel
Number Theory
Algebraic Geometry
11J81, 11J95, 11G10, 11G15
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 $A$.
title Hodge cycles and quadratic relations between holomorphic periods on CM abelian varieties
topic Number Theory
Algebraic Geometry
11J81, 11J95, 11G10, 11G15
url https://arxiv.org/abs/2411.12249