Isomorphism classes of abelian varieties over finite fields
2016 (English)Licentiate thesis, monograph (Other academic)
Deligne and Howe described polarized abelian varieties over finite fields in terms of finitely generated free Z-modules satisfying a list of easy to state axioms. In this thesis we address the problem of developing an effective algorithm to compute isomorphism classes of (principally) polarized abelian varieties over a finite field, together with their automorphism groups. Performing such computations requires the knowledge of the ideal classes (both invertible and non-invertible) of certain orders in number fields. Hence we describe a method to compute the ideal class monoid of an order and we produce concrete computations in dimension 2, 3 and 4.
Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University , 2016. , 64 p.
Algebraic Geometry, Abelian Varieties, Finite Fields, Ideal Class Group, Ideal Class Monoid
Geometry Algebra and Logic
IdentifiersURN: urn:nbn:se:su:diva-130316ISBN: 978-91-7649-444-8OAI: oai:DiVA.org:su-130316DiVA: diva2:929747
2016-06-13, 306, Kräftriket hus 6, Stockholm, 13:00 (English)
Halle, Lars, Associate Professor
Bergström, Jonas, Docent