On the arithmetic of an elliptic curve over a $Z_{p}$-extension

Franiçois Ramaroson

Displaying similar documents to “On the arithmetic of an elliptic curve over a $Z_{p}$ -extension”

Iwasawa theory for elliptic curves over imaginary quadratic fields

Massimo Bertolini (2001)

Journal de théorie des nombres de Bordeaux

Similarity:

Let $E$ be an elliptic curve over $ℚ$ , let $K$ be an imaginary quadratic field, and let $K_{\infty}$ be a $ℤ_{p}$ -extension of $K$ . Given a set $Σ$ of primes of $K$ , containing the primes above $p$ , and the primes of bad reduction for $E$ , write $K_{Σ}$ for the maximal algebraic extension of $K$ which is unramified outside $Σ$ . This paper is devoted to the study of the structure of the cohomology groups $H^{i} (K_{Σ} / K_{\infty}, E_{p^{\infty}})$ 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 $K_{\infty} / K .$ ...