TY - JOUR

T1 - Iwasawa theory for elliptic curves at supersingular primes

AU - Kobayashi, Shin Ichi

PY - 2003/7/4

Y1 - 2003/7/4

N2 - 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.

AB - 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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U2 - 10.1007/s00222-002-0265-4

DO - 10.1007/s00222-002-0265-4

M3 - Article

AN - SCOPUS:0038610569

VL - 152

SP - 1

EP - 36

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

SN - 0020-9910

IS - 1

ER -