Abelian varieties isogenous to a power of an elliptic curve over a\n Galois extension

2017/06/15 by Isabel Vogt, Vogt, Isabel
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1706.04963

Abstract

Given an elliptic curve E/k and a Galois extension k'/k, we construct an\nexact functor from torsion-free modules over the endomorphism ring rm\nEnd(E_k') with a semilinear rm Gal(k'/k) action to abelian varieties\nover k that are k'-isogenous to a power of E. As an application, we show\nthat every elliptic curve with complex multiplication geometrically is\nisogenous over the ground field to one with complex multiplication by a maximal\norder.\n

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