Counting integral points of bounded height on varieties with large fundamental group-Reference-Cited by-同舟云学术

Counting integral points of bounded height on varieties with large fundamental group

Published:2023-11-21 Issue:0 Volume:0 Page:
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Brunebarbe Yohan¹,Maculan Marco²

Affiliation:

1. Institut de Mathématiques de Bordeaux , Université de Bordeaux , 351 cours de la Libération, 33405 Talence , France

2. Institut de Mathématiques de Jussieu , Sorbonne Université , 4 place Jussieu, 75252 Paris , France

Abstract

Abstract The main result of this paper states the subpolynomial growth of the number of integral points with bounded height of a variety over a number field whose fundamental group is large. This generalizes a recent paper of Ellenberg, Lawrence and Venkatesh and replies to two questions asked therein.

Funder

Agence Nationale de la Recherche

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2023-0079/pdf

Reference41 articles.

1. B. Bakker, Y. Brunebarbe, B. Klingler and J. Tsimerman, Definability of mixed period maps, preprint (2020), https://arxiv.org/abs/2006.12403.

2. B. Bakker, Y. Brunebarbe and J. Tsimerman, o-minimal GAGA and a conjecture of Griffiths, Invent. Math. 232 (2023), no. 1, 163–228.

3. V. V. Batyrev and Y. Tschinkel, Rational points on some Fano cubic bundles, C. R. Acad. Sci. Paris Sér. I Math. 323 (1996), no. 1, 41–46.

4. A. Beauville, Le problème de Torelli, Séminaire Bourbaki. Volume 1985/86, 38ème année. Exposés Nos. 651–668, Astérisque 145/146, Société Mathématique de France, Paris (1987), 7–20.

5. P. Berthelot, A. Grothendieck, and L. Illusie Séminaire de Géométrie Algébrique du Bois-Marie 1966–1967 (SGA 6). Théorie des intersections et théorème de Riemann–Roch, Lecture Notes in Math. 225, Springer, Berlin 1971.