Mordell-Lang plus Bogomolov, by Bjorn Poonen

This paper, combined with 0128, has now appeared under the title ``Mordell-Lang plus Bogomolov'', in Invent. Math. 137 (1999), no. 2, 413-425, and so the preprint has been removed.

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.

Bjorn Poonen <>