On function field Mordell-Lang: the semiabelian case and the socle theorem

Abstract

We here aim to complete our model-theoretic account of the function field Mordell-Lang conjecture, avoiding appeal to dichotomy theorems for Zariski geometries, where we now consider the general case of semiabelian varieties. The main result is a reduction, using model-theoretic tools, of the semiabelian case to the abelian case.

43 pages. Some minor corrections and clarifications were made following a referee's report

References in corpus (2)

• Infinitely $p$-divisible points on abelian varieties defined over function fields of characteristic $p>0$
• Semiabelian varieties over separably closed fields, maximal divisible subgroups, and exact sequences