Genus of surcircular fields
Abstract
We show that Riemann-Hurwitz-style translation formulas obtained by Kuz'min, Kida, Iwasawa, Wingberg et alii for the lambda invariant attached to certain Iwasawa moduli in cyclotomic Z{\ell}-extension of number fields are essentially equivalent. More precisely, we prove that all these formulas,including those stated in terms of representations, resul tidentically for purely algebraic reasons from the arithmetic computation of a suitable Herbrand quotient which it suffices to carry out in the cyclic case of prime degree {\ell}.
Keywords
Cite
@article{arxiv.2104.02499,
title = {Genus of surcircular fields},
author = {Jean-François Jaulent},
journal= {arXiv preprint arXiv:2104.02499},
year = {2021}
}
Comments
in French. Le texte est la mise au format LATEX de l'article dactylographi{\'e} original paru aux Publications Math{\'e}matiques de Besan\c{c}on en 1986. Il n'en diff{\`e}re que par la correction de diverses coquilles,par l'harmonisation de quelques notations avec celles des articles ult{\'e}rieurs (notamment l'inversion de position de S et T) ainsi que par la num{\'e}rotation des th{\'e}or{\`e}mes