Integral points on algebraic subvarieties of period domains: from number fields to finitely generated fields-Reference-Cited by-同舟云学术

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

Published:2023-02-09 Issue:1-2 Volume:173 Page:23-44
ISSN:0025-2611
Container-title:manuscripta mathematica
language:en
Short-container-title:manuscripta math.

Author:

Javanpeykar Ariyan^ORCID,Litt Daniel

Abstract

AbstractWe 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

$$\mathbb {Z}$$

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 arithmetic locally symmetric varieties, the moduli space of smooth hypersurfaces in projective space, and the moduli of smooth divisors in an abelian variety.

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Link

https://link.springer.com/content/pdf/10.1007/s00229-023-01463-w.pdf

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