Abstract
We study finiteness problems for isogeny classes of abelian varieties over an algebraic function field K in one variable over the field of complex numbers. In particular, we construct explicitly a non-isotrivial absolutely simple abelian fourfold X over a certain K such that the isogeny class of X×X contains infinitely many mutually non-isomorphic principally polarized abelian varieties. (Such examples do not exist when the ground field is finitely generated over its prime subfield.)
Original language | English (US) |
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Pages (from-to) | 312-334 |
Number of pages | 23 |
Journal | Proceedings of the London Mathematical Society |
Volume | 96 |
Issue number | 2 |
DOIs | |
State | Published - Mar 2008 |
All Science Journal Classification (ASJC) codes
- General Mathematics