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- W4387338857 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." @default.
- W4387338857 created "2023-10-05" @default.
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- W4387338857 date "2020-10-07" @default.
- W4387338857 modified "2023-10-06" @default.
- W4387338857 title "On the fields of definition of Hodge loci" @default.
- W4387338857 doi "https://doi.org/10.48550/arxiv.2010.03359" @default.
- W4387338857 hasPublicationYear "2020" @default.
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