Moret-Bailly, Laurent Skolem problems on algebraic stacks. (Problèmes de Skolem sur les champs algébriques.) (French) Zbl 1106.11022 Compos. Math. 125, No. 1, 1-30 (2001). 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. Cited in 3 ReviewsCited in 9 Documents MSC: 11G35 Varieties over global fields 14G25 Global ground fields in algebraic geometry 14A20 Generalizations (algebraic spaces, stacks) Citations:Zbl 1003.11027; Zbl 0538.12014; Zbl 0581.14014; Zbl 0704.14015; Zbl 0704.14014 PDFBibTeX XMLCite \textit{L. Moret-Bailly}, Compos. Math. 125, No. 1, 1--30 (2001; Zbl 1106.11022) Full Text: DOI