Mikhail Borovoi, Tomer M. Schlank, “A cohomological obstruction to weak approximation for homogeneous spaces”, Mosc. Math. J., 2012, Volume 12, Number 1,Pages <nobr>1

This article is cited in 4 papers

A cohomological obstruction to weak approximation for homogeneous spaces

Mikhail Borovoi^a, Tomer M. Schlank^b

^a Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel
^b Institute of Mathematics, Hebrew University, Jerusalem, Israel

Abstract: Let $X$ be a homogeneous space, $X=G/H$, where $G$ is a connected linear algebraic group over a number field $k$, and $H\subset G$ is a $k$-subgroup (not necessarily connected). Let $S$ be a finite set of places of $k$. We compute a Brauer–Manin obstruction to weak approximation for $X$ in $S$ in terms of Galois cohomology.

Key words and phrases: Brauer–Manin obstruction, weak approximation, homogeneous spaces, linear algebraic groups, Brauer group, Galois cohomology.

MSC: Primary 14M17; Secondary 14G05, 20G10, 20G30

Received: January 19, 2011

Language: English

DOI: 10.17323/1609-4514-2012-12-1-1-20