EMIS/ELibM Electronic Journals

Outdated Archival Version

These pages are not updated anymore. They reflect the state of 22 June 2005. For the current production of this journal, please refer to http://intlpress.com/HHA/.


Stacks and the homotopy theory of simplicial sheaves

Stacks and the homotopy theory of simplicial sheaves

J.F. Jardine

Stacks are described as sheaves of groupoids $G$ satisfying an effective descent condition, or equivalently such that the classifying object $BG$ satisfies descent. The set of simplicial sheaf homotopy classes $[*,BG]$ is identified with equivalence classes of acyclic homotopy colimits fibred over $BG$, generalizing the classical relation between torsors and non-abelian cohomology. Group actions give rise to quotient stacks, which appear as parameter spaces for the separable transfer construction in special cases.


Homology, Homotopy and Applications, Vol. 3(2), 2001, pp. 361-384

http://www.rmi.acnet.ge/hha/volumes/2001/n2a5/v3n2a5.dvi (ps, dvi.gz, ps.gz, pdf)
ftp://ftp.rmi.acnet.ge/pub/hha/volumes/2001/n2a5/v3n2a5.dvi (ps, dvi.gz, ps.gz, pdf)