Iwasawa theory for elliptic curves at supersingular primes

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Abstract

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.

Original languageEnglish
Pages (from-to)1-36
Number of pages36
JournalInventiones Mathematicae
Volume152
Issue number1
DOIs
Publication statusPublished - Jul 4 2003
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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