Skip Navigation



Journal of the London Mathematical Society Advance Access published online on May 22, 2009
Journal of the London Mathematical Society, doi:10.1112/jlms/jdp021
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
80/1/135    most recent
jdp021v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Ellenberg, J. S.
Right arrow Articles by Kowalski, E.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2009 London Mathematical Society

Non-simple abelian varieties in a family: geometric and analytic approaches

Jordan S. Ellenberg

Department of Mathematics
University of Wisconsin
480 Lincoln Drive
Madison, WI 53705
USA
ellenber@math.wisc.edu

Christian Elsholtz

Department of Mathematics
Royal Holloway University of London
Egham
Surrey
TW20 0EX
United Kingdom
christian.elsholtz@rhul.ac.uk

Chris Hall

Department of Mathematics
University of Michigan
Ann Arbor MI 48109
USA
hallcj@umich.edu

Emmanuel Kowalski

ETH Zürich – D-MATH
Rämistrasse 101
8092 Zürich
Switzerland

We consider, in the special case of certain one-parameter families of Jacobians of curves defined over a number field, the problem of how the property that the generic fiber of such a family is absolutely simple ‘spreads’ to other fibers. We show that this question can be approached using arithmetic geometry or with more analytic methods based on sieve theory. In the first setting, non-trivial group-theoretic information is needed, while the version of the sieve we use is also of independent interest.

2000 Mathematics Subject Classification 11G10 (primary); 11N35, 14K15, 14D05 (secondary).

The first author was partially supported by NSF-Career grant DMS-0448750 and a Sloan Research Fellowship.

Received September 18, 2008; revised January 28, 2009;
Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.