A comparison of elliptic units in certain prime power conductor cases

Ulrich Schmitt

Acta Arithmetica (2015)

  • Volume: 171, Issue: 1, page 39-65
  • ISSN: 0065-1036

Abstract

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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, 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).

How to cite

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Ulrich Schmitt. "A comparison of elliptic units in certain prime power conductor cases." Acta Arithmetica 171.1 (2015): 39-65. <http://eudml.org/doc/286077>.

@article{UlrichSchmitt2015,
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 $_\{K\}$, 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).},
author = {Ulrich Schmitt},
journal = {Acta Arithmetica},
keywords = {elliptic units; Iwasawa theory; complex multiplication},
language = {eng},
number = {1},
pages = {39-65},
title = {A comparison of elliptic units in certain prime power conductor cases},
url = {http://eudml.org/doc/286077},
volume = {171},
year = {2015},
}

TY - JOUR
AU - Ulrich Schmitt
TI - A comparison of elliptic units in certain prime power conductor cases
JO - Acta Arithmetica
PY - 2015
VL - 171
IS - 1
SP - 39
EP - 65
AB - 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, 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).
LA - eng
KW - elliptic units; Iwasawa theory; complex multiplication
UR - http://eudml.org/doc/286077
ER -

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