Invariants and coinvariants of semilocal units modulo elliptic units

Stéphane Viguié[1]

  • [1] Université de Franche-Comté 16 route de Gray 25030 Besançon cedex, France

Journal de Théorie des Nombres de Bordeaux (2012)

  • Volume: 24, Issue: 2, page 487-504
  • ISSN: 1246-7405

Abstract

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Let p be a prime number, and let k be an imaginary quadratic number field in which p decomposes into two primes 𝔭 and 𝔭 ¯ . Let k ∞ be the unique ℤ p -extension of k which is unramified outside of 𝔭 , and let K ∞ be a finite extension of k ∞ , abelian over k . Let 𝒰 ∞ / 𝒞 ∞ be the projective limit of principal semi-local units modulo elliptic units. We prove that the various modules of invariants and coinvariants of 𝒰 ∞ / 𝒞 ∞ are finite. Our approach uses distributions and the p -adic L -function, as defined in [5].

How to cite

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Viguié, Stéphane. "Invariants and coinvariants of semilocal units modulo elliptic units." Journal de Théorie des Nombres de Bordeaux 24.2 (2012): 487-504. <http://eudml.org/doc/251078>.

@article{Viguié2012,
abstract = {Let $p$ be a prime number, and let $k$ be an imaginary quadratic number field in which $p$ decomposes into two primes $\mathfrak\{p\}$ and $\bar\{\mathfrak\{p\}\}$. Let $k_\infty $ be the unique $\mathbb\{Z\}_p$-extension of $k$ which is unramified outside of $\mathfrak\{p\}$, and let $K_\infty $ be a finite extension of $k_\infty $, abelian over $k$. Let $\mathcal\{U\}_\infty /\mathcal\{C\}_\infty $ be the projective limit of principal semi-local units modulo elliptic units. We prove that the various modules of invariants and coinvariants of $\mathcal\{U\}_\infty /\mathcal\{C\}_\infty $ are finite. Our approach uses distributions and the $p$-adic $\mathrm\{L\}$-function, as defined in [5].},
affiliation = {Université de Franche-Comté 16 route de Gray 25030 Besançon cedex, France},
author = {Viguié, Stéphane},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Iwasawa theory; main conjecture; imaginary quadratic number fields; semi-local units; elliptic units},
language = {eng},
month = {6},
number = {2},
pages = {487-504},
publisher = {Société Arithmétique de Bordeaux},
title = {Invariants and coinvariants of semilocal units modulo elliptic units},
url = {http://eudml.org/doc/251078},
volume = {24},
year = {2012},
}

TY - JOUR
AU - Viguié, Stéphane
TI - Invariants and coinvariants of semilocal units modulo elliptic units
JO - Journal de Théorie des Nombres de Bordeaux
DA - 2012/6//
PB - Société Arithmétique de Bordeaux
VL - 24
IS - 2
SP - 487
EP - 504
AB - Let $p$ be a prime number, and let $k$ be an imaginary quadratic number field in which $p$ decomposes into two primes $\mathfrak{p}$ and $\bar{\mathfrak{p}}$. Let $k_\infty $ be the unique $\mathbb{Z}_p$-extension of $k$ which is unramified outside of $\mathfrak{p}$, and let $K_\infty $ be a finite extension of $k_\infty $, abelian over $k$. Let $\mathcal{U}_\infty /\mathcal{C}_\infty $ be the projective limit of principal semi-local units modulo elliptic units. We prove that the various modules of invariants and coinvariants of $\mathcal{U}_\infty /\mathcal{C}_\infty $ are finite. Our approach uses distributions and the $p$-adic $\mathrm{L}$-function, as defined in [5].
LA - eng
KW - Iwasawa theory; main conjecture; imaginary quadratic number fields; semi-local units; elliptic units
UR - http://eudml.org/doc/251078
ER -

References

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