PUB - Publikationen an der Universität Bielefeld

For a noetherian scheme, we introduce its unbounded stable derived category.This leads to a recollement which reflects the passage from the bounded derivedcategory of coherent sheaves to the quotient modulo the subcategory of perfectcomplexes. Some applications are included, for instance an analogue of maximalCohen-Macaulay approximations, a construction of Tate cohomology, and anextension of the classical Grothendieck duality. In addition, the relevance ofthe stable derived category in modular representation theory is indicated.