Horrocks theory and the Bernstein-Gel'fand-Gel'fand correspondence

摘要

We construct an explicit equivalence between a category of complexes over the exterior algebra, which we call HT-complexes, and the stable category of vector bundles on the corresponding projective space, essentially translating into more fancy terms the results of Trautmann (1978) which, in turn, were influenced by ideas of Horrocks (1964), (1980). However, the result expressed by Theorem 5.1 and its corollary, which establishes a relation between the Tate resolutions over the exterior algebra ( described in a paper by Eisenbud, Floystad, and Schreyer) and HT-complexes, might be new, although, perhaps, not a surprise to experts.