The stable derived category of a noetherian scheme
Algebraic Geometry
2007-05-23 v3 Rings and Algebras
Representation Theory
Abstract
For a noetherian scheme, we introduce its unbounded stable derived category. This leads to a recollement which reflects the passage from the bounded derived category of coherent sheaves to the quotient modulo the subcategory of perfect complexes. Some applications are included, for instance an analogue of maximal Cohen-Macaulay approximations, a construction of Tate cohomology, and an extension of the classical Grothendieck duality. In addition, the relevance of the stable derived category in modular representation theory is indicated.
Cite
@article{arxiv.math/0403526,
title = {The stable derived category of a noetherian scheme},
author = {Henning Krause},
journal= {arXiv preprint arXiv:math/0403526},
year = {2007}
}
Comments
Final version, to appear in Compositio Math.; 38 pages