An algebraic version of a theorem of Kurihara
Robert Pollack
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(Qn) is finite and make precise statemens 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.
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