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Skolem problems on algebraic stacks. (Problèmes de Skolem sur les champs algébriques.) (French) Zbl 1106.11022

Summary: We extend R. S. Rumely’s local-global principle [J. Reine Angew. Math. 368, 127–133 (1986; Zbl 0581.14014)] (as refined by D. C. Cantor and P. Roquette [J. Number Theory 18, 1–26 (1984; Zbl 0538.12014)] 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.

MSC:

11G35 Varieties over global fields
14G25 Global ground fields in algebraic geometry
14A20 Generalizations (algebraic spaces, stacks)
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