A Galois theory with stable units for simplicial sets.
A generalization of a result on integers in metacyclic extensions
Let p be an odd prime and let c be an integer such that c>1 and c divides p-1. Let G be a metacyclic group of order pc and let k be a field such that pc is prime to the characteristic of k. Assume that k contains a primitive pcth root of unity. We first characterize the normal extensions L/k with Galois group isomorphic to G when p and c satisfy a certain condition. Then we apply our characterization to the case in which k is an algebraic number field with ring of integers ℴ, and, assuming some...
A generalization of Schinzel's theorem on radical extensions of fields and an application
A generalization of the Hasse-Arf theorem.
A hypercomplex proof of the Jordan-Kronecker's “Principle of reduction”
A projective invariant comparing rings of integers in wildly ramified extensions.
A propos de la relation galoisienne
L’existence d’un polynôme , irréductible sur un corps de caractéristique et dont trois racines vérifient la relation linéaire , ne dépend que de la paire de groupes finis où et est le fixateur d’une racine. Le cas régulier () est désormais assez bien décrit. On démontre dans ce texte que pour de nombreuses paires primitives ( sous-groupe maximal de ) et en particulier pour toutes celles de degré , la relation n’est pas réalisable.En appendice, Joseph Oesterlé démontre que cette...
A Recursive Description of the Maximal Pro-2 Galois Group Via Witt Rings.
A remark on real radical extensions
Abelian Extensions of Arbitrary Fields.
Abelian splitting of division algebras of prime degrees.
Algebraic dimension over Frobenius fields.
Algorithms for function fields.
Alternating group coverings of the affine line for characteristic greater than two.
An algorithmic construction of cyclic p-extensions of fields, with characteristic different from p, not containing the pth roots of unity
An Analogue of Artin-Schreier Theorem.
An analogue of Pfister's local-global principle in the burnside ring
Let be a Galois extension with Galois group . We study the set of -linear combinations of characters in the Burnside ring which give rise to -linear combinations of trace forms of subextensions of which are trivial in the Witt ring W of . In particular, we prove that the torsion subgroup of coincides with the kernel of the total signature homomorphism.
An arithmetic proof of Pop`s Theorem concerning Galois groups of function fields over number fields.
Anelli regolari separabilmente chiusi
Annihilating polynomials for quadratic forms.