An algebraic version of a theorem of Kurihara

Details An algebraic version of a theorem of Kurihara An algebraic version of a theorem of Kurihara

2004-07-22

arxiv.org/abs/math/0407393v1

Mathematics

Number Theory

Scientific paper

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 statemens 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.

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