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Abstract
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The paper formulates a precise relationship between the Tate–Shafarevich group of an elliptic
curve
over
with a quotient of
the class group of
on which
operates by its standard 2-dimensional representation over
. We
establish such a relationship in many cases.
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Keywords
class group, Tate–Shafarevich group, Selmer group, elliptic
curve, Galois cohomology
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Mathematical Subject Classification 2010
Primary: 11G05
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Milestones
Received: 30 December 2019
Revised: 16 December 2020
Accepted: 20 December 2020
Published: 4 August 2021
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