Supersingular elliptic curves over ℤ𝑝-extensions

IF 1.2 1区数学 Q1 MATHEMATICS Journal fur die Reine und Angewandte Mathematik Pub Date : 2023-06-15 DOI:10.1515/crelle-2023-0029

M. Çiperiani

引用次数: 0

Abstract

Abstract Let E / Q \mathrm{E}/\mathbb{Q} be an elliptic curve and 𝑝 a prime of supersingular reduction for E \mathrm{E} . Consider a quadratic extension L / Q p L/\mathbb{Q}_{p} and the corresponding anticyclotomic Z p \mathbb{Z}_{p} -extension L ∞ / L L_{\infty}/L . We analyze the structure of the points E ⁢ ( L ∞ ) \mathrm{E}(L_{\infty}) and describe two global implications of our results.

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超奇异椭圆曲线在0𝑝-extensions上

设E / Q \mathrm{E} / \mathbb{Q}为椭圆曲线，𝑝为E \mathrm{E}的超奇异约简素数。考虑一个二次扩展L/ Q p L/ \mathbb{Q} ＿p{和相应的抗细胞分裂Z p }\mathbb{Z} ＿p{ -扩展L∞/L L＿ }{\infty} /L。我们分析了E¹(L∞)\mathrm{E} (L＿ {\infty})点的结构，并描述了我们的结果的两个全局含义。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal fur die Reine und Angewandte Mathematik 数学-数学

CiteScore

2.50

自引率

6.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal für die reine und angewandte Mathematik is the oldest mathematics periodical still in existence. Founded in 1826 by August Leopold Crelle and edited by him until his death in 1855, it soon became widely known under the name of Crelle"s Journal. In the almost 180 years of its existence, Crelle"s Journal has developed to an outstanding scholarly periodical with one of the worldwide largest circulations among mathematics journals. It belongs to the very top mathematics periodicals, as listed in ISI"s Journal Citation Report.

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