Mordell-Lang plus Bogomolov

Abstract

We formulate a conjecture for semiabelian varieties A over number fields that includes both the Mordell-Lang conjecture (now proven) and the Bogomolov conjecture. We prove the "Mordellic" (finitely generated) part of the conjecture when A is isogenous to the product of an abelian variety and a torus. The proof makes use of the Mordell-Lang conjecture, the Bogomolov conjecture, and an equidistribution theorem.

6 pages, Latex 2e

Cited by in corpus (4)

• Relations among modular points on elliptic curves
• Non-dense sets of subvarieties in a power of an elliptic curve
• A Galois-dynamics correspondence for unicritical polynomials
• Uniform Mordell-Lang Plus Bogomolov