TY - JOUR

T1 - Vanishing of algebraic Brauer-Manin obstructions

AU - Borovoi, Mikhail

N1 - Funding Information:
Partially supported by the Hermann Minkowski Center for Geometry and by the Israel Science Foundation (grant 807/07).

PY - 2011/9

Y1 - 2011/9

N2 - Let X be a homogeneous space of a quasi-trivial k-group G, with geometric stabilizer H, over a number field k. We prove that under certain conditions on the character group of H, certain algebraic Brauer-Manin obstructions to the Hasse principle and weak approximation vanish, because the abelian groups where they take values vanish. When H is connected or abelian, these algebraic Brauer-Manin obstructions to the Hasse principle and weak approximation are the only ones, so we prove the Hasse principle and weak approximation for X under certain conditions. As an application, we obtain new sufficient conditions for the Hasse principle and weak approximation for linear algebraic groups.

AB - Let X be a homogeneous space of a quasi-trivial k-group G, with geometric stabilizer H, over a number field k. We prove that under certain conditions on the character group of H, certain algebraic Brauer-Manin obstructions to the Hasse principle and weak approximation vanish, because the abelian groups where they take values vanish. When H is connected or abelian, these algebraic Brauer-Manin obstructions to the Hasse principle and weak approximation are the only ones, so we prove the Hasse principle and weak approximation for X under certain conditions. As an application, we obtain new sufficient conditions for the Hasse principle and weak approximation for linear algebraic groups.

UR - http://www.scopus.com/inward/record.url?scp=84857444861&partnerID=8YFLogxK

M3 - מאמר

AN - SCOPUS:84857444861

VL - 26

SP - 333

EP - 349

JO - Journal of the Ramanujan Mathematical Society

JF - Journal of the Ramanujan Mathematical Society

SN - 0970-1249

IS - 3

ER -