VOL. 86 | 2020 Construction of elliptic p-units
Chapter Author(s) Werner Bley, Martin Hofer
Editor(s) Masato Kurihara, Kenichi Bannai, Tadashi Ochiai, Takeshi Tsuji
Adv. Stud. Pure Math., 2020: 79-111 (2020) DOI: 10.2969/aspm/08610079

Abstract

Let L/k be a finite abelian extension of an imaginary quadratic number field k. Let p denote a prime ideal of Ok lying over the rational prime p. We assume that p splits completely in L/k and that p does not divide the class number of k. If p is split in k/Q the first named author has adapted a construction of Solomon to obtain elliptic p-units in L. In this paper we generalize this construction to the non-split case and obtain in this way a pair of elliptic p-units depending on a choice of generators of a certain Iwasawa algebra (which here is of rank 2). In our main result we express the p-adic valuations of these p-units in terms of the p-adic logarithm of an explicit elliptic unit. The crucial input for the proof of our main result is the computation of the constant term of a suitable Coleman power series, where we rely on recent work of T. Seiriki.

Information

Published: 1 January 2020
First available in Project Euclid: 12 January 2021

Digital Object Identifier: 10.2969/aspm/08610079

Subjects:
Primary: 11G15 , 11G16 , 11R27

Keywords: Coleman power series , Elliptic units , Iwasawa theory

Rights: Copyright © 2020 Mathematical Society of Japan

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