Proceedings of the Japan Academy, Series A, Mathematical Sciences

On some Hasse principles for algebraic groups over global fields. III

Ngô Thị Ngoan and Nguyêñ Quôć Thǎńg

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Abstract

We establish some new local–global principles related with some splitting problems for connected linear algebraic groups over infinite algebraic extensions of global fields and give some applications to the isotropy problems. The main tools are certain new Hasse principles established for quadratic, (skew-)hermitian forms, and homogeneous projective spaces of reductive groups over such fields.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 92, Number 8 (2016), 87-91.

Dates
First available in Project Euclid: 3 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.pja/1475499413

Digital Object Identifier
doi:10.3792/pjaa.92.87

Mathematical Reviews number (MathSciNet)
MR3554861

Zentralblatt MATH identifier
06673659

Subjects
Primary: 11E72: Galois cohomology of linear algebraic groups [See also 20G10] 14F20: Étale and other Grothendieck topologies and (co)homologies 14L15: Group schemes
Secondary: 14G20: Local ground fields 20G10: Cohomology theory

Keywords
Hasse principle splitting field Tits index tori unipotent groups reductive groups

Citation

Ngoan, Ngô Thị; Thǎńg, Nguyêñ Quôć. On some Hasse principles for algebraic groups over global fields. III. Proc. Japan Acad. Ser. A Math. Sci. 92 (2016), no. 8, 87--91. doi:10.3792/pjaa.92.87. https://projecteuclid.org/euclid.pja/1475499413


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