summer 2000 



Sebastian Petersen, Universität Kassel 19.02.2020 12:00, B137 Title: Abelian varieties over ample fields of positive characteristic Abstract:
(Joint work with Arno Fehm) We will explain the proof of the following Theorem. Let K be an ample field which is not algebraic over a finite field. Then rank(A(K)) = ∞ for every nonzero abelian variety A/K. This is a common generalization of a variety of infinite rank results for abelian varieties over certain types of “large” fields. The theorem is known to be true in the case char(K) = 0 for a couple of years. The case char(K) > 0 is more involved, however, and could be established only recently. On the way we point out that a (slight generalization of) a recent theorem of Roessler together with work of GhiocaMoosa imply the dimension one case of the full MordellLang conjecture. Notes from the talk. 