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summer 2000
 
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Wojciech J. Gajda

professor of mathematics

Mailing address:
Faculty of Mathematics and Computer Science
Adam Mickiewicz University
Umultowska 87, 61-614 Poznań, POLAND
Office: Collegium Mathematicum, B1-35
Phone: +48 (61) 829 5503
Fax: +48 (61) 829 5315
Email: gajda AT amu DOT edu DOT pl

Research interests:

arithmetic geometry, number theory, algebraic topology, algebraic K-theory

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Sebastian Petersen, Universität Kassel

19.02.2020 12:00, B1-37

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 non-zero 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 Ghioca-Moosa imply the dimension one case of the full Mordell-Lang conjecture. Notes from the talk.