Homology, Homotopy and Applications

Volume 13 (2011)

Number 1

Cech approximation to the Brown-Gersten spectral sequence

Pages: 319 – 348

DOI: http://dx.doi.org/10.4310/HHA.2011.v13.n1.a13


Benjamin Antieau (Department of Mathematics, University of California at Los Angeles)


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

Full Text (PDF format)