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Selmer Groups over p ‐Adic Lie Extensions I
Author(s) -
Zerbes Sarah Livia
Publication year - 2004
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s002461070400568x
Subject(s) - mathematics , abelian group , elliptic curve , pure mathematics , abelian variety , conductor , group (periodic table) , division (mathematics) , algebraic number field , variety (cybernetics) , lie group , euler's formula , field (mathematics) , arithmetic , mathematical analysis , physics , geometry , quantum mechanics , statistics
Let E be an elliptic curve defined over a number field F. The paper concerns the structure of the p ∞ ‐Selmer group of E over p‐adic Lie extensions F ∞ of F which are obtained by adjoining to F the p‐division points of an abelian variety A defined over F. The main focus of the paper is the calculation of the Gal(F ∞F )‐Euler characteristic of the p ∞ ‐Selmer group of E. The main theory is illustrated with the example of an elliptic curve of conductor 294.