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Computing the Selmer group of an isogeny between Abelian varieties using a further isogeny to a Jacobian

✍ Scribed by Edward F. Schaefer; Joseph L. Wetherell


Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
224 KB
Volume
115
Category
Article
ISSN
0022-314X

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✦ Synopsis


This article describes an algorithm for computing the Selmer group of an isogeny between abelian varieties. This algorithm applies when there is an isogeny from the image abelian variety to the Jacobian of a curve. The use of an auxiliary Jacobian simplifies the determination of locally trivial cohomology classes. An example is presented where the rational solutions to x 4 + (y 2 + 1)(x + y) = 0 are determined.