Invariants and coinvariants of semilocal units modulo elliptic units
Journal de théorie des nombres de Bordeaux, Volume 24 (2012) no. 2, pp. 487-504.

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 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].

Soient p un nombre premier, et k un corps quadratique imaginaire dans lequel p se décompose en deux idéaux maximaux 𝔭 et 𝔭 ¯. Soit k l’unique p -extension de k non ramifiée en dehors de 𝔭, et soit K une extension finie de k , abélienne sur k. Soit 𝒰 /𝒞 la limite projective du module des unités semi-locales principales modulo le module des unités elliptiques. Nous prouvons que les différents modules des invariants et des co-invariants de 𝒰 /𝒞 sont finis. Notre approche utilise les distributions et la fonction L p-adique, définie dans [5].

DOI: 10.5802/jtnb.808
Viguié, Stéphane 1

1 Université de Franche-Comté 16 route de Gray 25030 Besançon cedex, France
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Viguié, Stéphane. Invariants and coinvariants of semilocal units modulo elliptic units. Journal de théorie des nombres de Bordeaux, Volume 24 (2012) no. 2, pp. 487-504. doi : 10.5802/jtnb.808. http://www.numdam.org/articles/10.5802/jtnb.808/

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