On function field Mordell-Lang and Manin-Mumford

We present a reduction of the function field Mordell-Lang conjecture to the function field Manin-Mumford conjecture, in all characteristics, via model theory, but avoiding recourse to the dichotomy theorems for (generalized) Zariski structures. In this version 2, the quantifier elimination result in positive characteristic is extended from simple abelian varieties to all abelian varieties, completing the main theorem in the positive characteristic case. In version 3, some corrections are made to the proof of quantifier elimination in positive characteristic, and the paper is substantially reorganized.Comment: 21 page

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

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.Comment: 43 pages. Some minor corrections and clarifications were made following a referee's repor

Imaginaries in separably closed valued fields

We show that separably closed valued fields of finite imperfection degree (either with lambda-functions or commuting Hasse derivations) eliminate imaginaries in the geometric language. We then use this classification of interpretable sets to study stably dominated types in those structures. We show that separably closed valued fields of finite imperfection degree are metastable and that the space of stably dominated types is strict pro-definable