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the stable derived category of a noetherian scheme

Published online by Cambridge University Press:  01 September 2005

henning krause
henning krause
Affiliation:
institut für mathematik, universität paderborn, 33095 paderborn, germanyhkrause@math.uni-paderborn.de
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Abstract

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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.

Keywords

stable categoryderived categorynoetherian schemegrothendieck dualitygorenstein injectivetate cohomology14f0518e30 (primary)16e4516g5055u35 (secondary)

Information

Type
Research Article
Information
Compositio Mathematica , Volume 141 , Issue 5 , September 2005 , pp. 1128 - 1162
Copyright
foundation compositio mathematica 2005