Fibred sites and stack cohomology

COHOMOLOGY ON SITES Contents

This is a chapter of the Stacks Project, version 7e38297, compiled on Feb 17, 2015.

COHOMOLOGY ON SITES Contents

This is a chapter of the Stacks Project, version 7dfc69e, compiled on Mar 23, 2015.

The Orbifold Cohomology Ring of Simplicial Toric Stack Bundles

We compute the orbifold cohomology ring of the simplicial toric stack bundles. We give an example to show that the ordinary cohomology ring of the crepant resolution of a simplicial toric stack bundle is not necessarily isomorphic to its orbifold cohomology ring.

Topological representation of sheaf cohomology of sites

For a site S (with enough points), we construct a topological space X(S) and a full embedding φ of the category of sheaves on S into those on X(S) (i.e., a morphism of toposes φ: Sh(X(S)) → Sh(S)). The embedding will be shown to induce a full embedding of derived categories, hence isomorphisms H(S, A) = H∗(X(S), φ A) for any abelian sheaf A on S. As a particular case, this will give for any sch...

Fibred and Virtually Fibred Hyperbolic 3-Manifolds in the Censuses