Groupe de Brauer non ramifié algébrique des espaces homogènes (The unramified algebraic Brauer group of homogeneous spaces)

Abstract

Using a reduction of the Galois cohomology of a linear algebraic group $G$ to that of a certain finite subquotient, we give different formulas allowing the calculation of the unramified algebraic Brauer group of a homogeneous space $V=G\backslash G^{\prime }$ with $G^{\prime }$ semisimple and simply connected, both over a finite field and over an arbitrary field of characteristic $0$.

30 pages. Text in French. Final version. Section and Theorem numbering now agree with the published article. arXiv admin note: text overlap with arXiv:1310.3663

References in corpus (1)

• Groupe de Brauer non ramifié des espaces homogènes à stabilisateur fini (Unramified Brauer group of homogeneous spaces with finite stabilizer)

Cited by in corpus (1)

• Extensions of algebraic groups with finite quotient and nonabelian 2-cohomology