A comparison of elliptic units in certain prime power conductor cases

Ulrich Schmitt¹

¹ M\"unchen, Germany

Acta Arithmetica, Tome 171 (2015) no. 1, pp. 39-65

Résumé

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).

Détail

DOI : 10.4064/aa171-1-4

Keywords: paper compare modules elliptic units which arise study elliptic curves quadratic imaginary fields complex multiplication mathcal ordinary reduction above split prime prime power conductor modules special those modules elliptic units studied nbsp rubin his paper invent math two variable main conjecture without p adic l functions other module smaller contained former studied nbsp nbsp yager ann math where connection p adic l functions given