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On Brauer--Manin obstructions and analogs of Cassels-Tate's exact sequence for connected reductive groups over global function fields.
- Source :
-
Proceedings of the Japan Academy, Series A: Mathematical Sciences . Nov2021, Vol. 97 Issue 9, p67-72. 6p. - Publication Year :
- 2021
-
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-Thelene) 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *LINEAR algebraic groups
*HOMOGENEOUS spaces
*BRAUER groups
Subjects
Details
- Language :
- English
- ISSN :
- 03862194
- Volume :
- 97
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Proceedings of the Japan Academy, Series A: Mathematical Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 153673074
- Full Text :
- https://doi.org/10.3792/pjaa.97.013