Isogeny classes of abelian varieties over function fields

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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 languageEnglish (US)
Pages (from-to)312-334
Number of pages23
JournalProceedings of the London Mathematical Society
Issue number2
StatePublished - Mar 2008

All Science Journal Classification (ASJC) codes

  • General Mathematics


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