Proc. Japan Acad. Ser. A Math. Sci. 92 (8), 87-91, (October 2016) DOI: 10.3792/pjaa.92.87
Ngô Thị Ngoan, Nguyêñ Quôć Thǎńg
KEYWORDS: Hasse principle, splitting field, Tits index, tori, unipotent groups, reductive groups, 11E72, 14F20, 14L15, 14G20, 20G10
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.