Homology, Homotopy and Applications
Volume 13 (2011)
Cech approximation to the Brown-Gersten spectral sequence
Pages: 319 – 348
In this paper, we show that the étale index of a torsion cohomological Brauer class is divisible by the period of the class. The tool used to make this computation is the Čech approximation of the title. To create the approximation, we use the folklore theorem that the homotopy limit and Postnikov spectral sequences for a cosimplicial space agree beginning with the $E_2$-page. As far we know, this folklore theorem has no proof in the literature, so we include a proof.
homotopy spectral sequence; cosimplicial space; Brauer group; twisted sheaf
2010 Mathematics Subject Classification
14F22, 16K50, 18G40, 19D23