Module de Frobenius et structure galoisienne des anneaux d’entiers. (French) Zbl 0468.12003

Cassou-Nogues, Ph.

J. Algebra 71, 268-289 (1981).

MSC:

11R32	Galois theory
11R42	Zeta functions and \(L\)-functions of number fields

Keywords:

algebraic integers; Frobenius module; Galois module structure; class group; Artin exponent

References:

[1]	Bass, H, Algebraic K-theory, (1968), Benjamin New York · Zbl 0174.30302
[2]	Cassou-Nogues, Ph, Structure galoisienne des anneaux d’entiers, (), 545-576 · Zbl 0425.12008
[3]	Cassou-Nogues, Ph, Théorèmes de base normale, (), exposé No. 27 · Zbl 0356.12011
[4]	Cassou-Nogues, Ph, Quelques théorèmes de base normale d’entiers, Ann. inst. Fourier (Grenoble), 3, 28, (1978) · Zbl 0368.12004
[5]	Cassou-Nogues, Ph, Groupe des classes de l’algèbre d’un groupe métacyclique, J. algebra, 1, (1976) · Zbl 0346.12010
[6]	Fröhlich, A, Arithmetic and Galois module structure for tame extensions, J. reine angew. math., 286/287, 380-439, (1976) · Zbl 0385.12004
[7]	Fröhlich, A, Galois module structure, algebraic number fields, () · Zbl 0375.12010
[8]	{\scA. Fröhlich}, Galois module structure and Root numbers for quaternion extensions of degré 2^{n}, à paraître. · Zbl 0469.12002
[9]	Galovich, S, The class group of a cyclic p-group, J. algebra, 30, 368-387, (1974) · Zbl 0282.13004
[10]	Jacobinski, H, On extensions of lattices, Michigan math. J., 13, 471-475, (1966) · Zbl 0143.05702
[11]	Lam, T.Y, Artin exponents of finite groups, J. algebra, 9, 94-119, (1968) · Zbl 0277.20006
[12]	Martinet, J, Character theory and Artin L-functions, () · Zbl 0359.12015
[13]	{\scA. Matchett}, Bimodule induced homomorphisms of locally free class-groups, J. Algebra, à paraître. · Zbl 0361.20007
[14]	{\scT. Miyata}, A normal integral basis theorem for dihedral groups, à paraître. · Zbl 0427.20005
[15]	Reiner, I, Projective class groups of symetric and alternating groups, Linear and multilinear algebra, 3, 115-121, (1975)
[16]	Swan, R.G; Evans, E.G, K-theory of finite groups and orders, ()
[17]	Taylor, M, Locally free class groups of groups of prime power order, J. algebra, 50, (1978) · Zbl 0377.20006
[18]	Taylor, M, On the self-duality of a ring of integers as a Galois module, Invent. math., 46, 173-177, (1978) · Zbl 0381.12007
[19]	Taylor, M, Galois module structure of relative abelian extensions, J. reine angew. math., 303/304, 97-101, (1978) · Zbl 0384.12007
[20]	Ullom, S, The exponent of class group, J. algebra, 29, 124-132, (1974) · Zbl 0278.20016
[21]	{\scS. Ullom}, Character action on the class group of Fröhlich, informal report.