A polynomial solution to regulation and tracking. I. Deterministic problem
A polynomial solution to regulation and tracking. II. Stochastic problem
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...
À propos d'un théorème de Frobenius
A question on the discriminants of involutions of central division algebras.
A quick and dirty irreducibility test for multivariate polynomials over .
A rational canonical form for matrix fields
A real nullstellensatz and positivstellensatz for the semipolynomials over an ordered field.
Let K be an ordered field and R its real closure. A semipolynomial will be defined as a function from Rn to R obtained by composition of polynomial functions and the absolute value. Every semipolynomial can be defined as a straight-line program containing only instructions with the following type: polynomial, absolute value, sup and inf and such a program will be called a semipolynomial expression. It will be proved, using the ordinary real positivstellensatz, a general real positivstellensatz concerning...
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 reciprocity law for K2-traces.
A Recursive Description of the Maximal Pro-2 Galois Group Via Witt Rings.
A remark on Ax's theorem on solvability modulo primes.
A remark on real radical extensions
A remark on the Chebotarev theorem about roots of unity.
A Remark on the Multidimensional Moment Problem.
A representation of models of Peano arithmetic
A representation theorem for a class of rigid analytic functions
Let be a prime number, the field of -adic numbers and the completion of the algebraic closure of . In this paper we obtain a representation theorem for rigid analytic functions on which are equivariant with respect to the Galois group , where is a lipschitzian element of and denotes the -neighborhood of the -orbit of .
A simple, (almost) non-inductive proof for the existence of composite fields and algebraic closures.