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A comparison of elliptic units in certain prime power conductor cases

Ulrich Schmitt (2015)

Acta Arithmetica

The aim of this paper is to compare two modules of elliptic units, which arise in the study of elliptic curves E over quadratic imaginary fields K with complex multiplication by $_{K}$ , good ordinary reduction above a split prime p and prime power conductor (over K). One of the modules is a special case of those modules of elliptic units studied by K. Rubin in his paper [Invent. Math. 103 (1991)] on the two-variable main conjecture (without p-adic L-functions), and the other module is a smaller one,...

A note on a product formula for the cubic Gauss sum

Hiroshi Ito (2012)

Acta Arithmetica

A refined cojecture of Mazur-Tate type for Heegner points.

Henri Darmon (1992)

Inventiones mathematicae

Annihilators of the class group of a compositum of quadratic fields

Jan Herman (2013)

Archivum Mathematicum

This paper is devoted to a construction of new annihilators of the ideal class group of a tamely ramified compositum of quadratic fields. These annihilators are produced by a modified Rubin’s machinery. The aim of this modification is to give a stronger annihilation statement for this specific type of fields.

Anticyclotomic Iwasawa theory of CM elliptic curves

Adebisi Agboola, Benjamin Howard (2006)

Annales de l’institut Fourier

We study the Iwasawa theory of a CM elliptic curve $E$ in the anticyclotomic $Z_{p}$ -extension of the CM field, where $p$ is a prime of good, ordinary reduction for $E$ . When the complex $L$ -function of $E$ vanishes to even order, Rubin’s proof of the two variable main conjecture of Iwasawa theory implies that the Pontryagin dual of the $p$ -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...