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.
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Oblatum 17-VI-2002 & 2-IX-2002¶Published online: 18 December 2002
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Kobayashi, Si. Iwasawa theory for elliptic curves at supersingular primes. Invent. math. 152, 1–36 (2003). https://doi.org/10.1007/s00222-002-0265-4
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DOI: https://doi.org/10.1007/s00222-002-0265-4