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2001•Compositio MathematicaOpen access

Problèmes de Skolem sur les champs algébriques

Laurent Moret-Bailly

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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.

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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.

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Available 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.

Key concepts: Mathematics, Pure mathematics, Algebraic number, Global field, Discrete mathematics, Mathematical analysis

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