Séminaires : Structures algébriques ordonnées

Equipe(s) : lm,
Responsables :F. Delon, M. Dickmann, D. Gondard
Email des responsables : dickmann@math.univ-paris-diderot.fr
Salle : 1016
Adresse :Sophie Germain

Mardi de 14h00 à 15h45
Page du séminaire et programme
Abonnement à la liste de diffusion

Orateur(s) Sylvy Anscombe - Univ. de Paris,
Titre Approximation for spaces of orderings and valuations
Horaire14:00 à 15:45
Diffusion Code: g27TmR
Résume(Joint work with Philip Dittmann and Arno Fehm.) By the classical Artin--Whaples approximation theorem we may simultaneously approximate finitely many different elements of a field with respect to finitely many pairwise inequivalent absolute values. Several variants and generalizations exist, for example for finitely many valuations, where one usually requires that these are independent (i.e. induce different topologies). Ribenboim proved a generalization for finitely many valuations where the condition of independence is relaxed for a natural compatibility condition, and Ershov proved a statement about simultaneously approximating finitely many different elements with respect to finitely many possibly infinite sets of pairwise independent valuations. We prove approximation theorems which generalize both of these: we work with infinite sets of valuations and orderings and we weaken the requirement of pairwise independence. On the way we'll use the notation of a `locality', generalising both valuations and orderings. We will discuss the space of localities and explore some advantages and deficiencies of this approach.
AdresseZoom ID 844 2542 2716