Signed-Selmer Groups over the Z2p-extension of an Imaginary Quadratic Field

Kim, Byoung Du (B. D.)

Canadian journal of mathematics, Tome 66 (2014) no. 4, pp. 826-843

Résumé

Let $E$ be an elliptic curve over $\mathbb{Q}$ that has good supersingular reduction at $p\,>\,3$ . We construct what we call the $\pm /\pm $ -Selmer groups of $E$ over the $\mathbb{Z}_{p}^{2}$ -extension of an imaginary quadratic field $K$ when the prime $p$ splits completely over $K/\mathbb{Q}$ , and prove that they enjoy a property analogous to Mazur's control theorem.Furthermore, we propose a conjectural connection between the $\pm /\pm $ -Selmer groups and Loeffler's two-variable $\pm /\pm $ - $p$ -adic $L$ -functions of elliptic curves.

Détail

DOI : 10.4153/CJM-2013-043-2

Mots-clés : 11D45, 11P55, 11T55, elliptic curves, Iwasawa theory

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