The equivariant Tamagawa number conjecture and modular symbols
The equivariant Tamagawa number conjecture and modular symbols
复制标题
等变玉川数猜想和模符号
DOI：
10.1007/s00208-012-0837-6
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发表时间：
2012
影响因子：
1.4
通讯作者：
W. Bley
中科院分区：
文献类型：
--
作者：
W. Bley
证明了对每条椭圆曲线，都有以下条件：对每条椭圆曲线，\Docentclass[12pt]{minimum}\usepackage{amsath}\usepackage{wa ysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{mathsfs}\usepackage{upgreek}\setlong{\oddsidemargin}{-69pt}\Begin{Document}$$E/\mathbb q$\end{Document}with\DocumentClass[12pt]{Minimum}\usepackage{amsath}\usepackage{asepackage{amsfonts}\usepackage{amssb\}Usepackage{amsbsy}\usepackage{mathsf}\usepackage{upgreek}\setlong{\oddsidemargin}{-69pt}\Begin{Document}$$L(E/\mathbb q，1)\n 0$$\end{Document}有无限多个奇素数\Documentclass[12pt]{Minimum}\usepackage{amsath}\usepackage{waysym}\usepackage{amsFonts}\usepackage{amsbsy}\usepackage{mathsfs}\usepackage{upgreek}\setlong{\oddsidemargin}{-69pt}\Begin{Document}$$L$\end{Document}以及对于每个这样的\DocumentClass[12pt]{Minimum}\usepackage{amsath}\usepackage{amssym}\usepackage{amsts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsbsy}\usepackage{upgreek}\setlong{\oddsidemargin}{-69pt}\Begin{文档}$$L$\end{Document}无限多个abelian\Documentclass[12pt]{minimum}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amssymb}\usepackage{upgreek}\setlong{\oddsidemargin}{-69pt}\Begin{Document}$$L$\end{文档}-扩展\DocumentClass[12pt]{Minimum}\usepackage{amsath}\usepackage{wa ysym}\usepackage{amsfonts}\usepackage{amsbsy}\usepackage{mathsfs}\usepackage{upgreek}\setlong{\oddsidemargin}{-69pt}\Begin{Document}$K/\mathbb Q$\end{Document}使得\DocumentClass[12pt]{Minimum}\usepackage{amsath}\usepackage{waysym\usepackage{amsfonts}\usepackage{amssymb}Usepackage{amsbsy}\usepackage{mathrsf}\usepackage{upgreek}\setLong{\oddsidemargin}{-69pt}\Begin{Document}$$L$$\end{Document}-等变Tamagawa数猜想的一部分适用于以下对：\Documentclass[12pt]{minimum}\usepackage{amsath}\usepackage{waysym}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{upgreek}\setlong{odsidemargin}{-69pt}\Begin{Document$}$(h^1(E_K)(1)，(1)\mathbb Z[\Text{Gal}(K/\mathbb Q)])$$\end{文档}。
We show that for each elliptic curve \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E/\mathbb Q $$\end{document} with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L(E/\mathbb Q , 1) \ne 0$$\end{document} there are infinitely many odd primes \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l$$\end{document} and for each such \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l$$\end{document} infinitely many abelian \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l$$\end{document}-extensions \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K/\mathbb Q $$\end{document} such that the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l$$\end{document}-part of the equivariant Tamagawa number conjecture holds for the pair \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(h^1(E_K)(1), \mathbb Z [\text{ Gal}(K/\mathbb Q )])$$\end{document}.