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A comparison of elliptic units in certain prime power conductor cases

Volume 171 / 2015

Ulrich Schmitt Acta Arithmetica 171 (2015), 39-65 MSC: Primary 11G16; Secondary 11R23, 14K22. DOI: 10.4064/aa171-1-4

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).

Authors

  • Ulrich SchmittM\"unchen, Germany
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