A note on perfect modules over crossed products
À propos des théories de Galois finies et infinies
Abelsche Galoiserweiterungen von R[X].
Anelli regolari separabilmente chiusi
Anneau des entiers d'une extension galoisienne considéré comme module sur l'algèbre du groupe de Galois
Conducteurs d'Artin des caractères réels.
Décomposition du Galois-module des entiers d'une extension cyclique de degré premier d'un corps local ou d'un corps de nombres
Décomposition du Galois-module des entiers d'une extension cyclique de degré premier d'un corps de nombres ou d'un corps local
Soit un anneau de Dedekind, de corps des fractions , et soit une extension galoisienne de , dont le groupe de Galois est cyclique d’ordre premier. On note la clôture intégrale de dans . Il existe une unique décomposition du -module en somme directe de sous-modules indécomposables. On détermine cette décomposition lorsque est un corps local ou un corps de nombres. Le résultat dépend d’une part des caractères irréductibles de sur , d’autre part des nombres de ramification associés...
Degeneration of the Kummer sequence in characteristic
We study a deformation of the Kummer sequence to the radicial sequence over an -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.
Diskriminanten und Picard-Invarianten freier quadratischer Erweiterungen.
Etale covers, bimodules and differential operators.
Extension of semiclean rings
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.
Factorial extensions of regular local rings and invariants of finite groups.
Galois actions on rings and finite Galois coverings.
Galois theory and Lubin-Tate cochains on classifying spaces
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 , the cochain extension is not a Galois...
Galois theory of commutative rings revisited.
Homotopy representability of Brauer groups.
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.
Konstruktion von zusammenhängenden galoisschen Algebren der Charakteristik pk zu vorgegebener Gruppe der Ordnung pf.
Lifting solutions over Galois rings.
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.
Noether's problem over an algebraically closed field.