2021 ADELIC DOUBLE COSETS OVER SEMI-GLOBAL FIELDS
David Harbater
Author Affiliations +
Albanian J. Math. 15(2): 99-115 (2021). DOI: 10.51286/albjm/1636109898

Abstract

Double coset spaces of adelic points on linear algebraic groups arise in the study of global fields; e.g., concerning local-global principles and torsors. A different type of double coset space plays a role in the study of semi-global fields such as p-adic function fields. This paper relates the two, by establishing adelic double coset spaces over semi-global fields; relating them to local-global principles and torsors; and providing explicit examples.

Funding Statement

The author was supported in part by NSF grant DMS-2102987.

Citation

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David Harbater. "ADELIC DOUBLE COSETS OVER SEMI-GLOBAL FIELDS." Albanian J. Math. 15 (2) 99 - 115, 2021. https://doi.org/10.51286/albjm/1636109898

Information

Published: 2021
First available in Project Euclid: 11 July 2023

MathSciNet: MR4346264
zbMATH: 1490.11045
Digital Object Identifier: 10.51286/albjm/1636109898

Subjects:
Primary: 11E72 , 12G05 , 14G05
Secondary: 14G27 , 14H25 , 20G15

Keywords: class sets , double cosets , Galois cohomology , linear algebraic groups , local-global principles , patching , semi-global fields , torsors

Rights: Copyright © 2021 Research Institute of Science and Technology (RISAT)

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Vol.15 • No. 2 • 2021
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