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arXiv · 1903.08007

A comparison between obstructions to local-global principles over semiglobal fields

David Harbater·Julia Hartmann·Valentijn Karemaker·Florian Pop
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Abstract

We consider local-global principles for rational points on varieties, in particular torsors, over one-variable function fields over complete discretely valued fields. There are several notions of such principles, arising either from the valuation theory of the function field, or from the geometry of a regular model of the function field. Our results compare the corresponding obstructions, proving in particular that a local-global principle with respect to valuations implies a local-global principle with respect to a sufficiently fine regular model.

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David Harbater, Julia Hartmann, Valentijn Karemaker, Florian Pop. 2019-03-19. A comparison between obstructions to local-global principles over semiglobal fields. https://arxiv.org/abs/1903.08007

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