Quadratic forms over fraction fields of two-dimensional Henselian rings and Brauer groups of related schemes. (English) Zbl 1055.14019

Colliot-Thélène, J.-L.; Ojanguren, M.; Parimala, R.

Parimala, R. (ed.), Proceedings of the international colloquium on algebra, arithmetic and geometry, Mumbai, India, January 4–12, 2000. Part I and II. New Delhi: Narosa Publishing House, published for the Tata Institute of Fundamental Research, Bombay (ISBN 81-7319-476-9). Stud. Math., Tata Inst. Fundam. Res. 16, 185-217 (2002).

The authors present several results on Brauer groups which generalize to homogeneous spaces of connected linear algebraic groups over a base field. They conclude the paper with two conjectures pertaining to the aforementioned spaces.
For the entire collection see [Zbl 1013.00021].

Reviewer: Richard A. Mollin (Calgary)

MSC:

14F22	Brauer groups of schemes
11E99	Forms and linear algebraic groups

Keywords:

division algebras; unramified; isotropic quadratic forms