Abstract: The Bernstein-Gelfand-Gelfand (BGG) correspondence is a an equivalence between the derived categories of graded modules over a polynomial ring and exterior algebra, respectively. Eisenbud, Fl\/oystad and Schreyer (2003) derive an explicit version of the BGG correspondence that, among other things, clarifies the relationship between free resolutions of graded modules over the exterior algebra and the cohomology of coherent sheaves on projective space.

On the other hand, work of Jan-Erik Roos and Maurice Auslander gives a filtration of a graded module over a polynomial ring with supports that decrease in dimension, via a suitable Grothendieck spectral sequence. I will describe some joint work with Hal Schenck in which we consider the interplay between these two constructions. We find applications to some topological spaces with cohomology rings generated in degree 1.