# Problèmes de Skolem sur les champs algébriques

Research paper by Laurent Moret-Bailly

Indexed on: 01 Jan '01Published on: 01 Jan '01Published in: Compositio Mathematica

#### Abstract

We extend Rumely's local-global principle (as refined by Cantor, Roquette, and the author, i.e. with local splitting conditions) to the case of algebraic stacks, in Artin's sense, over rings of (S-)integers of global fields. The nongeometrically connected case is also taken into account, as well as (in some instances) the case where local conditions are imposed at all places.