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The fine Tate–Shafarevich group

Published online by Cambridge University Press:  12 February 2007

Séction de mathématiques, CSAG, École Polytechnique Fédérale, 1015 Lausanne, Switzerland.


Within the Tate–Shafarevich group of an elliptic curve E defined over a number field K, there is a canonical subgroup defined by imposing stronger conditions at the places above a given prime p. This group appears naturally in the Iwasawa theory for E. We propose a study of what one can say about the relation to the full Tate–Shafarevich group. Some numerical examples are included, as well as a few conjectures.

Research Article
Copyright © Cambridge Philosophical Society 2007

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