Abelian surfaces admitting an (l,l)-endomorphism

Details Abelian surfaces admitting an (l,l)-endomorphism Abelian surfaces admitting an (l,l)-endomorphism

2011-06-09

arxiv.org/abs/1106.1884v1

Mathematics

Algebraic Geometry

25 pages

Scientific paper

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.

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