• Corpus ID: 117027553

Sur la théorie du corps de classes dans les corps finis et les corps locaux

  title={Sur la th{\'e}orie du corps de classes dans les corps finis et les corps locaux},
  author={Claude Chevalley},
The Chevalley–Gras formula over global fields
In this article we give an adelic proof of the Chevalley-Gras formula for global fields, which itself is a generalization of the ambiguous class number formula. The idea is to reduce the formula to
Iwasawa Invariants of Some Non-Cyclotomic $\mathbb Z_p$-extensions
Iwasawa showed that there are non-cyclotomic $\mathbb Z_p$-extensions with positive $\mu$-invariant. We show that these $\mu$-invariants can be evaluated explicitly in many situations when $p=2$ and
On S-ramified T-split Iwasawa modules
We correct the faulty formulas given in a previous article and we compute the defect group for the Iwasawa λ invariants attached to the S-ramified T -decomposed abelian pro-l-extensions on the
Die mathematischen Tagebücher von Helmut Hasse 1923 - 1935
ISBN 978-3-86395-072-9 Le m m er m ey er / R oq ue tte D ie m at he m at is ch en T ag eb uc he r vo n He lm ut H as se 1 92 3 19 3T book contains the full text of the mathematical notebooks of
Demushkin groups and inverse Galois theory for pro-p-groups of finite rank and maximal p-extensions
This paper proves that if $E$ is a field, such that the Galois group $\mathcal{G}(E(p)/E)$ of the maximal $p$-extension $E(p)/E$ is a Demushkin group of finite rank $r(p)_{E} \ge 3$, for some prime
Sur la trivialit{\'e} de certains modules d'Iwasawa
We discuss the triviality of some classical Iwasawa modules in connection with the notion of l-rationality for totally l-adic number fields.
. In this paper, we consider the real pure quartic number field K = Q ( 4 (cid:112) pd 2 ) , where p is a prime number and d is a square-free positive integer such that d is prime to p . We compute r
Greenberg's conjecture for real quadratic fields and the cyclotomic $\mathbb{Z}_2$-extensions
Let An be the 2-part of the ideal class group of the n-th layer of the cyclotomic Z2-extension of a real quadratic number field F . The cardinality of An is related to the index of cyclotomic units
Application of the notion of $\varphi$-object to the study of $p$-class groups and $p$-ramified torsion groups of abelian extensions
We revisit, in an elementary way, the statement of the “Main Conjecture for p-class groups”, in abelian fields K, in the non semi-simple case p | [K : Q]; for this, we use an “arithmetic” definition