Abstract
Answering a question of Moshe Jarden we construct over every global fieldK examples of embedding problems which are locally solvable everywhere but not globally solvable. The construction is based on the results of an old paper of Hoechsmann of 1967.
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References
K. Hoechsmann,Zum Einbettungsproblem, Journal für die Reine und Angewandte Mathematik229 (1967), 81–106.
F. Lorenz and P. Roquette,On the theorem of Grunwald-Wang in the setting of valuation theory, inValuation Theory and its Applications, Volume II (Proceedings of an International Conference and Workshop, University of Saskatchewan, Saskatoon, Canada, July 28–August 11, 1999) (F.-V. Kuhlmann et al., eds.), Fields Institute Communications33 (2003), 175–212.
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Roquette, P. On the local-global principle for embedding problems over global fields. Isr. J. Math. 141, 369–379 (2004). https://doi.org/10.1007/BF02772229
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DOI: https://doi.org/10.1007/BF02772229