An algebraic version of a theorem of Kurihara

Robert Pollack

doi:10.1016/j.jnt.2003.10.008

An algebraic version of a theorem of Kurihara

Robert Pollack

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

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 Tamagawa 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.

Original language	English (US)
Pages (from-to)	164-177
Number of pages	14
Journal	Journal of Number Theory
Volume	110
Issue number	1
DOIs	https://doi.org/10.1016/j.jnt.2003.10.008
State	Published - Jan 2005
Externally published	Yes

Keywords

Elliptic curves
Iwasawa theory
Supersingular primes

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jnt.2003.10.008

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AB - 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 Tamagawa factors for E are all prime to p. Under these hypotheses, we prove that E(Qn) is finite and make precise statements about the size and structure of the p-power part of III (E/Qn). Here Qn is the n-th step in the cyclotomic Zp-extension of Q.

KW - Elliptic curves

KW - Iwasawa theory

KW - Supersingular primes

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JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 1

ER -

An algebraic version of a theorem of Kurihara

Abstract

Keywords

ASJC Scopus subject areas

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