Signed-Selmer Groups over the ℤ2 p-extension of an Imaginary Quadratic Field
Signed-Selmer Groups over the ℤ2 p-extension of an Imaginary Quadratic Field
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DOI：
10.4153/cjm-2013-043-2
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发表时间：
2014-08
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通讯作者：
Byoung Du (B. D.) Kim
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文献类型：
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作者：
Byoung Du (B. D.) Kim
Abstract 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.
