The stable derived category of a noetherian scheme

Details The stable derived category of a noetherian scheme The stable derived category of a noetherian scheme

2004-03-30

arxiv.org/abs/math/0403526v3

Mathematics

Algebraic Geometry

Final version, to appear in Compositio Math.; 38 pages

Scientific paper

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.

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