Work

Abelian surfaces admitting an (l,l)-endomorphism

Year: 2011

Type: preprint

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

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1106.1884

Authors: Broker, Reinier, Lauter, Kristin, Streng, Marco

Institutions: Brown University, Microsoft (United States), Leiden University, Vrije Universiteit Amsterdam

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Microsoft Research, Engineering and Physical Sciences Research Council

Award: Algorithms for Algebraic Number Theory

OpenAlex ID: W1976574349

Cites: 13

Cited by: 1

Related to: 20