On proper surjections with locally trivial Leray sheaves

A characterization of sheaf-trivial, proper maps with cohomologically locally connected images

Let f : X-, Y be a proper surjection of locally compact metric spaces. Throughout, the Leray sheafs of f are assumed to be (locally) trivial either in all dimensions or through a given dimension. Using a spectral sequence, the cohomological local connectivity of Y is analyzed and thus characterized by the structure of f. We define f to be cohomologically locally connected if, for each y E Y, ne...

Locally Free Sheaves

In these talks we will discuss several important examples of locally free sheaves and see the connection between locally free sheaves and finitely generated projective modules. In addition, we will see the connection between the divisor class group and the Picard group (aka ideal class group) of a domain. The bulk of this talk is taken from Sections 5 and 6 of Chapter II of [3]. Proofs of the v...

Locally trivial W∗-bundles

SHEAVES: FROM LERAY TO GROTHENDIECK AND SATO by

— We show how the ideas of Leray (sheaf theory), Grothendieck (derived categories) and Sato (microlocal analysis) lead to the microlocal theory of sheaves which allows one to reduce many problems of linear partial differential equations to problems of microlocal geometry. Moreover, sheaves on Grothendieck topologies are a natural tool to treat growth conditions which appear in Analysis. Résumé ...

Extending locally truncated chamber systems by sheaves

We generalize the theory of sheaves to chamber systems. We prove that, given a chamber system C and a family R of proper residues of C containing all residues of rank c1, every sheaf defined over R admits a completion which extends C. We also prove that, under suitable hypotheses, a sheaf defined over a truncation of C can be extended to a sheaf for C. In the last section of this paper, we appl...