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Search: MSC category 11Gxx ( Arithmetic algebraic geometry (Diophantine geometry) [See also 11Dxx, 14Gxx, 14Kxx] )

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1. CJM 2013 (vol 66 pp. 826)

Kim, Byoung Du
Signed-Selmer Groups over the $\mathbb{Z}_p^2$-extension of an Imaginary Quadratic Field
Let $E$ be an elliptic curve over $\mathbb Q$ which has good supersingular reduction at $p\gt 3$. 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 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.

Keywords:elliptic curves, Iwasawa theory

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