Iwasawa theory for elliptic curves at supersingular primes

研究成果: ジャーナルへの寄稿記事

63 引用 (Scopus)

抄録

We give a new formulation in Iwasawa theory for elliptic curves at good supersingular primes. This formulation is similar to Mazur's at good ordinary primes. Namely, we define a new Selmer group, and show that it is of Λ-cotorsion. Then we formulate the Iwasawa main conjecture as that the characteristic ideal is generated by Pollack's p-adic L-function. We show that this main conjecture is equivalent to Kato's and Perrin-Riou's main conjectures. We also prove an inequality in the main conjecture by using Kato's Euler system. In terms of the λ- And the μ-invariants of our Selmer group, we specify the numbers λ and μ in the asymptotic formula for the order of the Tate-Shafarevich group by Kurihara and Perrin-Riou.

元の言語英語
ページ(範囲)1-36
ページ数36
ジャーナルInventiones Mathematicae
152
発行部数1
DOI
出版物ステータス出版済み - 7 4 2003
外部発表Yes

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Iwasawa Theory
Elliptic Curves
Selmer Group
P-adic L-function
Euler System
Formulation
Asymptotic Formula
Invariant

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

これを引用

Iwasawa theory for elliptic curves at supersingular primes. / Kobayashi, Shin Ichi.

:: Inventiones Mathematicae, 巻 152, 番号 1, 04.07.2003, p. 1-36.

研究成果: ジャーナルへの寄稿記事

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