Let $E$ be an elliptic curve over $mathbb{Q}$, let $K$ be an imaginary quadratic field, and let $K_ infty$ be a $mathbb{Z}_p$-extension of $K$. Given a set $Sigma$ of primes of $K$, containing the primes above $p$, and the primes of bad reduction for $E$, write $K_Sigma$ for the maximal algebraic extension of $K$ which is unramified outside $Sigma$. This paper is devoted to the study of the structure of the cohomology groups $H^i (K_Sigma / K_infty, E_{p^ infty})$ for $i = 1, 2,$ and of the $p$-primary Selmer group Sel$_{p^ infty}(E / K_infty)$, viewed as discrete modules over the Iwasawa algebra of $K_infty / K.$

Iwasawa theory for elliptic curves over imaginary quadratic fields / M. Bertolini. - In: JOURNAL DE THÉORIE DES NOMBRES DE BORDEAUX. - ISSN 1246-7405. - 13:1(2001), pp. 1-25. [10.5802/jtnb.300]

Iwasawa theory for elliptic curves over imaginary quadratic fields

M. Bertolini
2001

Abstract

Let $E$ be an elliptic curve over $mathbb{Q}$, let $K$ be an imaginary quadratic field, and let $K_ infty$ be a $mathbb{Z}_p$-extension of $K$. Given a set $Sigma$ of primes of $K$, containing the primes above $p$, and the primes of bad reduction for $E$, write $K_Sigma$ for the maximal algebraic extension of $K$ which is unramified outside $Sigma$. This paper is devoted to the study of the structure of the cohomology groups $H^i (K_Sigma / K_infty, E_{p^ infty})$ for $i = 1, 2,$ and of the $p$-primary Selmer group Sel$_{p^ infty}(E / K_infty)$, viewed as discrete modules over the Iwasawa algebra of $K_infty / K.$
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/177499
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