English

Abelian surfaces admitting an (l,l)-endomorphism

Algebraic Geometry 2013-02-13 v2 Number Theory

Abstract

We give a classification of all principally polarized abelian surfaces that admit an (l,l)(l,l)-isogeny to themselves, and show how to compute all the abelian surfaces that occur. We make the classification explicit in the simplest case l=2l=2. As part of our classification, we also show how to find all principally polarized abelian surfaces with multiplication by a given imaginary quadratic order.

Keywords

Cite

@article{arxiv.1106.1884,
  title  = {Abelian surfaces admitting an (l,l)-endomorphism},
  author = {Reinier Broker and Kristin Lauter and Marco Streng},
  journal= {arXiv preprint arXiv:1106.1884},
  year   = {2013}
}

Comments

25 pages

R2 v1 2026-06-21T18:20:10.836Z