Instytut Matematyczny Polskiej Akademii Nauk / Institute of Mathematics / Publishing house / Journals and Serials / Acta Arithmetica / All issues

Abstract

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 $\mathcal {O}_{K}$, 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, contained in the former, as studied by R. I. Yager in [Ann. of Math. 115 (1982)] (where a connection to $p$-adic $L$-functions is given).