Inventiones mathematicae

, Volume 152, Issue 1, pp 1–36

Iwasawa theory for elliptic curves at supersingular primes

  • Shin-ichi Kobayashi

DOI: 10.1007/s00222-002-0265-4

Cite this article as:
Kobayashi, Si. Invent. math. (2003) 152: 1. doi:10.1007/s00222-002-0265-4


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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Shin-ichi Kobayashi
    • 1
  1. 1.Graduate School of Mathematical Sciences, University of Tokyo, Komaba 3-8-1, Tokyo, 153-8914 Japan (e-mail: