A local-global principle for similarities over function fields of p-adic curves

Let p∈N be a prime with p≠2, and let K be a p-adic field. Let F be the function field of a curve over K. Let ΩF be the set of all divisorial discrete valuations of F. In this paper, we ask whether the Hasse principle holds for semisimple adjoint linear algebraic groups over F. We give a positive ans...

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Bibliographic Details
Published in:Journal of algebra 2025-02, Vol.663, p.435-453
Main Author: Barlow, Jack
Format: Article
Language:English
Subjects:
Adjoint groups
Local-global principle
Semi-global fields
Similitudes
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Summary:Let p∈N be a prime with p≠2, and let K be a p-adic field. Let F be the function field of a curve over K. Let ΩF be the set of all divisorial discrete valuations of F. In this paper, we ask whether the Hasse principle holds for semisimple adjoint linear algebraic groups over F. We give a positive answer to this question for a class of adjoint classical groups.
ISSN:0021-8693
DOI:10.1016/j.jalgebra.2024.08.038