Ordinary Abelian Varieties: Isogeny Graphs and Polarizations

HAL 2026 Preprint Open access

Read full text
Authors: Edgar Costa, Taylor Dupuy, Stefano Marseglia, David Roe, Christelle Vincent
Cited by: 0

Abstract

Given an integer D and an ordinary isogeny class of abelian varieties defined over a finite field Fq with commutative Fq-endomorphism algebra, we provide algorithms for computing all isogenies of degree dividing D and polarizations of degree dividing D. We discuss phenomena that arise for higher dimension abelian varieties but not elliptic curves, bounds on the diameter of the graph of minimal isogenies, and decompositions of isogeny graphs into orbits for the Picard group of the Frobenius order.

Fields of Study & Subjects

Algebraic Geometry and Number Theory Advanced Algebra and Geometry Rings Modules and Algebras

Publication details

Journal / source
HAL
Publication date
2 February 2026
Language
EN
Document type
Preprint