Une formule pour le groupe de Brauer algébrique d'un torseur

Details Une formule pour le groupe de Brauer algébrique d'un torseur Une formule pour le groupe de Brauer algébrique d'un torseur

2010-11-23

arxiv.org/abs/1011.5100v1

Mathematics

Algebraic Geometry

32 pages

Scientific paper

For a homogeneous space X of a connected algebraic group G (with connected stabilizers) over a field k of characteristic zero, we construct a canonical complex of Galois modules of length 3 and a canonical isomorphism between an 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.

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