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arXiv · 1011.5100

Une formule pour le groupe de Brauer alg\'ebrique d'un torseur

Cyril Demarche
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Abstract

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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Cyril Demarche. 2010-11-23. Une formule pour le groupe de Brauer alg\'ebrique d'un torseur. https://arxiv.org/abs/1011.5100

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