Let be a prime number, and let be an imaginary quadratic number field in which decomposes into two primes and . Let be the unique -extension of which is unramified outside of , and let be a finite extension of , abelian over . Let be the projective limit of principal semi-local units modulo elliptic units. We prove that the various modules of invariants and coinvariants of are finite. Our approach uses distributions and the -adic -function, as defined in [5].
Soient un nombre premier, et un corps quadratique imaginaire dans lequel se décompose en deux idéaux maximaux et . Soit l’unique -extension de non ramifiée en dehors de , et soit une extension finie de , abélienne sur . Soit 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 sont finis. Notre approche utilise les distributions et la fonction -adique, définie dans [5].
@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/} }
TY - JOUR TI - Invariants and coinvariants of semilocal units modulo elliptic units JO - Journal de Théorie des Nombres de Bordeaux PY - 2012 DA - 2012/// SP - 487 EP - 504 VL - 24 IS - 2 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.808/ UR - https://zbmath.org/?q=an%3A1272.11079 UR - https://www.ams.org/mathscinet-getitem?mr=2950704 UR - https://doi.org/10.5802/jtnb.808 DO - 10.5802/jtnb.808 LA - en ID - JTNB_2012__24_2_487_0 ER -
Stéphane Viguié. 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. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.808/
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