On the fields of definition of Hodge loci

IF 1.3 1区 数学 Q1 MATHEMATICS
Bruno Klingler, Anna Otwinowska, David Urbanik
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引用次数: 3

Abstract

A polarizable variation of Hodge structure over a smooth complex quasi projective variety $S$ is said to be defined over a number field $L$ if $S$ and the algebraic connection associated to the variation are both defined over $L$. Conjecturally any special subvariety (also called an irreducible component of the Hodge locus) for such variations is defined over $\overline{\mathbb{Q}}$, and its Galois conjugates are also special subvarieties. We prove this conjecture for special subvarieties satisfying a simple monodromy condition. As a corollary we reduce the conjecture that special subvarieties for variation of Hodge structures defined over a number field are defined over $\overline{\mathbb{Q}}$ to the case of special points.
霍奇位点的定义领域
如果$S$和与之相关的代数联系都定义在$L$上,那么在光滑复拟射影变量$S$上的Hodge结构的可极化变分是定义在$L$上的。在$\overline{\mathbb{Q}}$上定义了这些变分的任何特殊子变分(也称为Hodge轨迹的不可约分量),其伽罗瓦共轭也是特殊子变分。我们对满足简单单态条件的特殊子变种证明了这个猜想。作为一个推论,我们将在$\overline{\mathbb{Q}}$上定义的在数域上定义的Hodge结构的变分的特殊子变量的猜想约化为特殊点的情况。
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来源期刊
CiteScore
3.00
自引率
5.30%
发文量
25
审稿时长
>12 weeks
期刊介绍: The Annales scientifiques de l''École normale supérieure were founded in 1864 by Louis Pasteur. The journal dealt with subjects touching on Physics, Chemistry and Natural Sciences. Around the turn of the century, it was decided that the journal should be devoted to Mathematics. Today, the Annales are open to all fields of mathematics. The Editorial Board, with the help of referees, selects articles which are mathematically very substantial. The Journal insists on maintaining a tradition of clarity and rigour in the exposition. The Annales scientifiques de l''École normale supérieures have been published by Gauthier-Villars unto 1997, then by Elsevier from 1999 to 2007. Since January 2008, they are published by the Société Mathématique de France.
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