Compositio Mathematica

the stable derived category of a noetherian scheme

henning krause a1
a1 institut für mathematik, universität paderborn, 33095 paderborn, germany

Article author query
krause h   [Google Scholar] 


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.

(Received April 22 2004)
(Accepted September 24 2004)
(Published Online September 1 2005)

Key Words: stable category; derived category; noetherian scheme; grothendieck duality; gorenstein injective; tate cohomology.

Maths Classification

14f05; 18e30 (primary); 16e45; 16g50; 55u35 (secondary).

dedicated to claus michael ringel on the occasion of his 60th birthday