Signed-Selmer Groups over the Z2p-extension of an Imaginary Quadratic Field
Canadian journal of mathematics, Tome 66 (2014) no. 4, pp. 826-843
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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.
Kim, Byoung Du (B. D.). Signed-Selmer Groups over the Z2p-extension of an Imaginary Quadratic Field. Canadian journal of mathematics, Tome 66 (2014) no. 4, pp. 826-843. doi: 10.4153/CJM-2013-043-2
@article{10_4153_CJM_2013_043_2,
author = {Kim, Byoung Du (B. D.)},
title = {Signed-Selmer {Groups} over the {Z2p-extension} of an {Imaginary} {Quadratic} {Field}},
journal = {Canadian journal of mathematics},
pages = {826--843},
year = {2014},
volume = {66},
number = {4},
doi = {10.4153/CJM-2013-043-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2013-043-2/}
}
TY - JOUR AU - Kim, Byoung Du (B. D.) TI - Signed-Selmer Groups over the Z2p-extension of an Imaginary Quadratic Field JO - Canadian journal of mathematics PY - 2014 SP - 826 EP - 843 VL - 66 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2013-043-2/ DO - 10.4153/CJM-2013-043-2 ID - 10_4153_CJM_2013_043_2 ER -
%0 Journal Article %A Kim, Byoung Du (B. D.) %T Signed-Selmer Groups over the Z2p-extension of an Imaginary Quadratic Field %J Canadian journal of mathematics %D 2014 %P 826-843 %V 66 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2013-043-2/ %R 10.4153/CJM-2013-043-2 %F 10_4153_CJM_2013_043_2
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