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Abelian surfaces admitting an $$(l,l)$$-endomorphism. (English) Zbl 1316.14085
Summary: 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.

##### MSC:
 14K02 Isogeny 14C20 Divisors, linear systems, invertible sheaves
Echidna
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