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

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].

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].

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DOI : https://doi.org/10.5802/jtnb.808
@article{JTNB_2012__24_2_487_0,
     author = {St\'ephane Vigui\'e},
     title = {Invariants and coinvariants of semilocal units modulo elliptic units},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {487--504},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {24},
     number = {2},
     year = {2012},
     doi = {10.5802/jtnb.808},
     zbl = {1272.11079},
     mrnumber = {2950704},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.808/}
}
Stéphane Viguié. Invariants and coinvariants of semilocal units modulo elliptic units. Journal de Théorie des Nombres de Bordeaux, Tome 24 (2012) no. 2, pp. 487-504. doi : 10.5802/jtnb.808. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.808/

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