Integral points on algebraic subvarieties of period domains: from number fields to finitely generated fields

Ariyan Javanpeykar; Daniel Litt

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arXiv · 1907.13536

Integral points on algebraic subvarieties of period domains: from number fields to finitely generated fields

Ariyan Javanpeykar·Daniel Litt

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Abstract

We show that for a variety which admits a quasi-finite period map, finiteness (resp.~non-Zariski-density) of $S$-integral points implies finiteness (resp.~non-Zariski-density) of points over all $\mathbb{Z}$-finitely generated integral domains of characteristic zero. Our proofs rely on foundational results in Hodge theory due to Deligne, Griffiths, and Schmid, and Bakker-Brunebarbe-Tsimerman. We give straightforward applications to Shimura varieties, locally symmetric varieties, the moduli space of smooth hypersurfaces in projective space, and the moduli of smooth divisors in an abelian variety.

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BibTeX RIS

Ariyan Javanpeykar, Daniel Litt. 2019-07-31. Integral points on algebraic subvarieties of period domains: from number fields to finitely generated fields. https://arxiv.org/abs/1907.13536

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