A characterization of locally compact fields of zero characteristic
A complete parametriziation of cyclic field extensions of 2-power degree.
A constructive Approach to Noether's Problem.
A counterexample to a conjecture of multinomial degree
A Galois theory with stable units for simplicial sets.
A GAP package for braid orbit computation and applications.
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 Hauptsatz of L. E. Dickson and Artin-Schreier extensions.
A hypercomplex proof of the Jordan-Kronecker's “Principle of reduction”
A monogenic Hasse-Arf theorem
I extend the Hasse–Arf theorem from residually separable extensions of complete discrete valuation rings to monogenic extensions.
A Note on the Normality of Unramified, Abelian Extensions of Quadratic Extensions.
A problem on coefficient fields and equations over local rings
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 rational canonical form for matrix fields
A really elementary proof of real Lüroth's theorem.
Classical Lüroth theorem states that every subfield K of K(t), where t is a transcendental element over K, such that K strictly contains K, must be K = K(h(t)), for some non constant element h(t) in K(t). Therefore, K is K-isomorphic to K(t). This result can be proved with elementary algebraic techniques, and therefore it is usually included in basic courses on field theory or algebraic curves. In this paper we study the validity of this result under weaker assumptions: namely, if K is a subfield...
A Recursive Description of the Maximal Pro-2 Galois Group Via Witt Rings.
A remark on real radical extensions