On finite Λ-submodules of Selmer groups of elliptic curves
On finite Λ-submodules of Selmer groups of elliptic curves
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椭圆曲线 Selmer 群的有限 Λ 子模
DOI：
10.1090/s0002-9939-00-05452-6
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
Kazuo Matsuno
中科院分区：
文献类型：
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作者：
Y. Hachimori;Kazuo Matsuno
本文给出了R. Greenberg关于Selmer群的非平凡有限a子模不存在的另一个证明。设p是质数。设K是一个数域，E是定义在K上的椭圆曲线。对于任意代数扩展L/K和L的任意位置v，我们用Lv表示L中所有有限扩展K在v处的补全并。Lv) L的一个固定代数闭包。Lv)，并固定浸渍L -* Lv。则E /L的p′-Selmer群定义为Selpoo (EIL) = Ker (H1 (Gal(L/L), Epoo) fJ H1 (Gal(Lv/Lv)， E(Lv))，
In this note, we give another proof of a result of R. Greenberg on the non-existence of non-trivial finite A-submodules of Selmer groups. Let p be a prime number. Let K be a number field and E an elliptic curve defined over K. For any algebraic extension L/K and any place v of L, we denote by Lv the union of the completions at v of all finite extensions of K contained in L. We further denote by L (resp. Lv) a fixed algebraic closure of L (resp. Lv), and fix an immersion L -* Lv. Then the p'-Selmer group of E over L is defined as Selpoo (EIL) = Ker (H1 (Gal(L/L), Epoo) fJ H1 (Gal(Lv/Lv), E(Lv))),