Drinfeld’s relative compactification plays a basic role in the theory of automorphic sheaves, and its singularities encode representation-theoretic information in the form of intersection cohomology. We introduce a resolution of singularities consisting of stable maps from nodal deformations of the curve into twisted flag varieties. As an application, we prove that the twisted intersection coho...

A discrete group with word-length (G,L) is B -isocohomological for a bounding classes B if the comparison map from B -bounded cohomology to ordinary cohomology (with coefficients in C) is an isomorphism; it is strongly B isocohomological if the same is true with arbitrary coefficients. In this paper we establish some basic conditions guaranteeing strong B -isocohomologicality. In particular, we...

We discuss the geometry of string and M-theory gauge fields in Deligne cohomology. In particular, we show how requiring string structure (or loop space Spin structure) on the five brane leads to topological conditions on the flux in the relative Deligne cohomology of the bulk brain pair. PACS 11.25.-w

In this paper we show that the Baues-Wirsching complex used to define cohomology of categories is a 2-functor from a certain 2-category of natural systems of abelian groups to the 2-category of chain complexes, chain homomorphism and relative homotopy classes of chain homotopies. As a consequence we derive (co)localization theorems for this cohomology.