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November 2021 On Brauer–Manin obstructions and analogs of Cassels–Tate’s exact sequence for connected reductive groups over global function fields
Nguyễn Quốc Thắng
Proc. Japan Acad. Ser. A Math. Sci. 97(9): 67-72 (November 2021). DOI: 10.3792/pjaa.97.013

Abstract

We show that the Brauer–Manin obstructions to the Hasse principle and weak approximation for homogeneous spaces under connected reductive groups over global function fields with connected reductive stabilizers are the only ones, extending some of Borovoi’s results (and thus also proving a partial case of a conjecture of Colliot-Thélène) in this regard. Along the way, we extend some perfect pairings and an important local-global exact sequence (an analog of a Cassels–Tate’s exact sequence) proved by Sansuc for connected linear algebraic groups defined over number fields, to the case of connected reductive groups over global function fields and beyond.

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Nguyễn Quốc Thắng. "On Brauer–Manin obstructions and analogs of Cassels–Tate’s exact sequence for connected reductive groups over global function fields." Proc. Japan Acad. Ser. A Math. Sci. 97 (9) 67 - 72, November 2021. https://doi.org/10.3792/pjaa.97.013

Information

Published: November 2021
First available in Project Euclid: 4 November 2021

Digital Object Identifier: 10.3792/pjaa.97.013

Subjects:
Primary: 11E72, 14G20
Secondary: 20G10

Rights: Copyright © 2021 The Japan Academy

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Vol.97 • No. 9 • November 2021
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