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We study the Iwasawa theory of a CM elliptic curve in the anticyclotomic -extension of the CM field, where is a prime of good, ordinary reduction for . When the complex -function of vanishes to even order, Rubin’s proof of the two variable main conjecture of Iwasawa theory implies that the Pontryagin dual of the -power Selmer group over the anticyclotomic extension is a torsion Iwasawa module. When the order of vanishing is odd, work of Greenberg show that it is not a torsion module. In...
The ring of projective invariants of ordered points on the projective line is one of the most basic and earliest studied examples in Geometric Invariant Theory. It is a remarkable fact and the point of this paper that, unlike its close relative the ring of invariants of unordered points, this ring can be completely and simply described. In 1894 Kempe found generators for this ring, thereby proving the First Main Theorem for it (in the terminology introduced by Weyl). In this paper we compute...
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