An algebraic version of a theorem of Kurihara

JOURNAL OF NUMBER THEORY

卷:110

Article

Pollack, R

关键词: elliptic curves;    Iwasawa theory;    supersingular primes;   

DOI  :  10.1016/j.jnt.2003.10.008

来源: Elsevier

【 摘 要 】

Let E/Q be an elliptic curve and let p be an odd supersingular prime for E. In this article, we study the simplest case of Iwasawa theory for elliptic curves, namely when E(Q) is finite, III(E/Q) has no p-torsion and the Tantagawa factors for E are all prime to p. Under these hypotheses, we prove that E(Q(n)) is finite and make precise statements about the size and structure of the p-power part of III(E/Q(n)). Here Q(n) is the n-th step in the cyclotomic Z(p)-extension of Q. (C) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

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