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Ramification in p-Adic Lie Extensions.
Rapport sur le prolongement analytique dans les corps values complets par la méthode des éléments analytiques quasi-connexes
Rapports de produits croulants
Rationals with exotic convergences. II.
Real commutative algebra (I). Places.
Real commutative algebra (II). Plane curves.
Real commutative algebra. III. Dedekind-Weber-Riemann manifolds.
The space S of all non-trivial real places on a real function field K|k of trascendence degree one, endowed with a natural topology analogous to that of Dedekind and Weber's Riemann surface, is shown to be a one-dimensional k-analytic manifold, which is homeomorphic with every bounded non-singular real affine model of K|k. The ground field k is an arbitrary ordered, real-closed Cantor field (definition below). The function field K|k is thereby represented as a field of real mappings of S which might...
Recent results in the theory of constant reductions
Reciprocity in valued function fields.
Reduction of semialgebraic constructible functions
Let R be a real closed field with a real valuation v. A ℤ-valued semialgebraic function on Rⁿ is called algebraic if it can be written as the sign of a symmetric bilinear form over R[X₁,. .., Xₙ]. We show that the reduction of such a function with respect to v is again algebraic on the residue field. This implies a corresponding result for limits of algebraic functions in definable families.
Relative Spectral Norm on Algebraic Numbers
Relatively complete ordered fields without integer parts
We prove a convenient equivalent criterion for monotone completeness of ordered fields of generalized power series with exponents in a totally ordered Abelian group G and coefficients in an ordered field F. This enables us to provide examples of such fields (monotone complete or otherwise) with or without integer parts, i.e. discrete subrings approximating each element within 1. We include a new and more straightforward proof that is always Scott complete. In contrast, the Puiseux series field...
Remarks on Banach- -algebras. (Remarques sur les -algèbres de Banach.)
Remarks on existentially closed fields and diophantine equations
Remarks on the Composite G-valuations and their Hypermetric Properties
Remarks on the Pythagoras and Hasse number of real fields.
Répartition des zéros et des pôles d'une fonction analytique
Répartition modulo 1 dans un corps de séries formelles sur un corps fini
Introduction. Soit q une puissance d’un nombre premier p et soit le corps fini à q éléments. Une certaine analogie entre l’arithmétique de l’anneau ℤ des entiers rationnels et celle de l’anneau a conduit à étendre à de nombreuses questions de l’arithmétique classique. L’équirépartition modulo 1 est une de ces questions. Le corps des nombres réels est alors remplacé par le corps des séries de Laurent formelles, complété du corps des fractions rationnelles pour la valuation à l’infini et...
Representation by quadratic forms in valuation rings