The bounded height conjecture for semiabelian varieties

authored by

Lars Kühne

Abstract

The bounded height conjecture of Bombieri, Masser, and Zannier states that for any sufficiently generic algebraic subvariety of a semiabelian -variety there is an upper bound on the Weil height of the points contained in its intersection with the union of all algebraic subgroups having (at most) complementary dimension in. This conjecture has been shown by Habegger in the case where is either a multiplicative torus or an abelian variety. However, there are new obstructions to his approach if is a general semiabelian variety. In particular, the lack of Poincaré reducibility means that quotients of a given semiabelian variety are intricate to describe. To overcome this, we study directly certain families of line bundles on. This allows us to demonstrate the conjecture for general semiabelian varieties.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

Type

Article

Journal

Compositio mathematica

Pages

1405-1456

No. of pages

52

ISSN

0010-437X

Publication date

2020

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Algebra and Number Theory

Electronic version(s)

https://doi.org/10.48550/arXiv.1703.03891 (Access: Open)
https://doi.org/10.1112/S0010437X20007198 (Access: Closed)