论文标题
在霍奇基因座的定义领域
On the fields of definition of Hodge loci
论文作者
论文摘要
如果$ s $，则可以在数字字段$ l $上定义霍奇结构的两极分化变化，如果$ s $和与变体相关的代数连接都定义在$ l $上。 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在$ \ overline {\ mathbb {q}} $上定义了在数字字段上定义的hodge结构变化的子变量。
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.
