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

Abstract

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.

Locations

• Journal of the London Mathematical Society - View
• reroDoc Digital Library - View - PDF
• arXiv (Cornell University) - View - PDF
• Deep Blue (University of Michigan) - View - PDF
• Repository for Publications and Research Data (ETH Zurich) - View - PDF