A formula for the Brauer group of an algebraic torso

作者：Demarche Cyril^*

来源：Journal of Algebra, 2011, 347(1): 96-132.

DOI：10.1016/j.jalgebra.2011.09.003

• Brauer group
• Homogeneous space
• Torsors

Given a homogeneous space X of a connected algebraic group G (with connected stabilizers) over a field k of characteristic zero, we construct a complex of Galois modules of length 3 and a canonical isomorphism between a hypercohomology group of this complex and an explicit subgroup of the Brauer group of X. This result is obtained as a consequence of a formula describing the "algebraic Brauer group of a torsor", and it generalizes recent results by Borovoi and van Hamel, by considering non-linear groups G and by taking into account some transcendental elements in the Brauer group of X.

• 出版日期2011-12-1