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Décomposition du Galois-module des entiers d'une extension cyclique de degré premier d'un corps de nombres ou d'un corps local

Françoise Bertrandias (1979)

Annales de l'institut Fourier

Soit A un anneau de Dedekind, de corps des fractions K , et soit L une extension galoisienne de K , dont le groupe de Galois G est cyclique d’ordre premier. On note B la clôture intégrale de A dans L . Il existe une unique décomposition du A [ G ] -module B en somme directe de sous-modules indécomposables. On détermine cette décomposition lorsque K est un corps local ou un corps de nombres. Le résultat dépend d’une part des caractères irréductibles de G sur K , d’autre part des nombres de ramification associés...

Degeneration of the Kummer sequence in characteristic p > 0

Yuji Tsuno (2010)

Journal de Théorie des Nombres de Bordeaux

We study a deformation of the Kummer sequence to the radicial sequence over an 𝔽 p -algebra, which is somewhat dual for the deformation of the Artin-Schreier sequence to the radicial sequence, studied by Saidi. We also discuss some relations between our sequences and the embedding of a finite flat commutative group scheme into a connected smooth affine commutative group schemes, constructed by Grothendieck.

Extension of semiclean rings

Chahrazade Bakkari, Mohamed Es-Saidi, Najib Mahdou, Moutu Abdou Salam Moutui (2022)

Czechoslovak Mathematical Journal

This paper aims at the study of the notions of periodic, UU and semiclean properties in various context of commutative rings such as trivial ring extensions, amalgamations and pullbacks. The results obtained provide new original classes of rings subject to various ring theoretic properties.

Galois theory and Lubin-Tate cochains on classifying spaces

Andrew Baker, Birgit Richter (2011)

Open Mathematics

We consider brave new cochain extensions F(BG +,R) → F(EG +,R), where R is either a Lubin-Tate spectrum E n or the related 2-periodic Morava K-theory K n, and G is a finite group. When R is an Eilenberg-Mac Lane spectrum, in some good cases such an extension is a G-Galois extension in the sense of John Rognes, but not always faithful. We prove that for E n and K n these extensions are always faithful in the K n local category. However, for a cyclic p-group C p r , the cochain extension F ( B C p r + , E n ) F ( E C p r + , E n ) is not a Galois...

Homotopy representability of Brauer groups.

Antonio Martínez Cegarra (1999)

Extracta Mathematicae

The purpose of this paper is to present certain facts and results showing a way through which simplicial homotopy theory can be used in the study of Auslander-Goldman-Brauer groups of Azumaya algebras over commutative rings.

Lifting solutions over Galois rings.

Javier Gómez-Calderón (1990)

Extracta Mathematicae

In this note we generalize some results from finite fields to Galois rings which are finite extensions of the ring Zpm of integers modulo pm where p is a prime and m ≥ 1.

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