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Local-global principle for over semiglobal fields

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arxiv 2406.17355 v2 pith:DFYIMMBZ submitted 2024-06-25 math.AG math.NT

Philippe Gille (ICJ , AGL , IMAR) , Raman Parimala This is my paper · ORCID
classification math.AGmath.NT
keywords local-globalprinciplesemiglobalcomparecompletionsdefineddifferentdivisorial
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We compare different local-global principles for torsors under a reductive group G defined over a semiglobal field F. In particular if the F-group G s a retract rational F-variety, we prove that the local global principle holds for the completions with respect to divisorial valuations of F.

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  1. Loop torsors. Theory and applications

    math.AG 2024-12 conditional novelty 7.0 of 10

    Toral torsors are loop, and loop torsors are toral, for extensions of twisted constant groups by reductive groups over Laurent polynomial rings in arbitrary characteristic, with sharp counterexamples.

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