Groupe de Brauer non ramifi\'e des espaces homog\`enes \`a stabilisateur fini (Unramified Brauer group of homogeneous spaces with finite stabilizer)

Abstract

We develop different formulas of algebraic and/or arithmetic nature allowing an explicit calculation, both over a finite field and over a field of characteristic 0, of the algebraic part of the unramified Brauer group of a homogeneous space G\G' under a semisiple simply connected linear group G' with finite stabilizer G. We also give examples of the calculations that can be done with these formulas.