Atlas Mathematical Conference Abstracts ||
Conferences |
Abstracts |
for Organizers |
About AMCA
Canadian Number Theory Association VIII Meeting
June 20-25, 2004
The Fields Institute
Toronto, ON, Canada |
|
Organizers
John Friedlander (Toronto) and Cam Stewart (Waterloo)
View Abstracts
Conference Homepage |
On a Question of Jarden and Frey about Ranks of Abelian Varieties
by
Sebastian Petersen
Universität der Bundeswehr, München
Let A an abelian variety over a field k. We shall say that A is
of FJ type iff A(kab) has infinite rank. 1974 Frey and Jarden
asked if any nonzero abelian variety over a number field is of FJ type.
Rosen and Wong recently verified this for the Jacobians of cyclic covers of P1 over a number field k. We generalize their work by allowing an arbitrary Hilbert field k as ground field
(note that this includes the function field case), and
treating a broader class of abelian varieties (including nonzero
isogeny factors of Albanese varieties of abelian covers of Pn).
Furthermore we discuss related work, carrying over results of
Gouvéa, Mazur, Stewart, Top, Rubin and Silverberg on ranks
of twists of elliptic curves to the case of twists of cyclic covers of
P1.
Date received: April 30, 2004
Copyright © 2004 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Mathematical Conference Abstracts.
Document # caok-05.