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1 results

  • the stable derived category of a noetherian scheme

  • henning krause
  • Journal:
    Compositio Mathematica / Volume 141 / Issue 5 / September 2005
    Published online by Cambridge University Press:
    01 September 2005, pp. 1128-1162
    Print publication:
    September 2005
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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.