1. Abelian surfaces admitting an -endomorphism.
- Author
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Bröker, Reinier, Lauter, Kristin, and Streng, Marco
- Subjects
- *
ABELIAN groups , *GEOMETRIC surfaces , *ENDOMORPHISM rings , *QUADRATIC equations , *MULTIPLICATION , *MATHEMATICAL proofs - Abstract
Abstract: We give a classification of all principally polarized abelian surfaces that admit an -isogeny to themselves, and show how to compute all the abelian surfaces that occur. We make the classification explicit in the simplest case . As part of our classification, we also show how to find all principally polarized abelian surfaces with multiplication by a given imaginary quadratic order. [Copyright &y& Elsevier]
- Published
- 2013
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