On a group graded version of BGG

摘要

A major result in Algebraic Geometry is the theorem of Bernstein-Gelfand-Gelfand that states the existence of an equivalence of triangulated categories: (gr) under bar (Lambda) congruent to D-b(Coh P-n), where (gr) under bar (Lambda) denotes the stable category of finitely generated graded modules over the n + 1 exterior algebra and D-b(Coh P-n) is the derived category of bounded complexes of coherent sheaves on projective space P-n. Generalizations of this result were obtained in Martinez-Villa and Saorin (2004) and from a different point of view, the theorem has been extended by Yanagawa (2004) to Z(n)-graded modules over the polynomial algebra. This generalization has important applications in combinatorial commutative algebra. The aim of the article is to extend the results of Martinez-Villa and Saorin (2004) to group graded algebras in order to obtain a generalization of Yanagawa's results having in mind the application to other settings (Geigle and Lenzing, 1987).