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On the simple object associated to a diagram in a closed model category

Published online by Cambridge University Press:  24 October 2008

Pere Pascual-Gainza
Pere Pascual-Gainza
Affiliation:
Departament de Matematiques, Universitat Politecnica de Catalunya, 08028 Barcelona, Spain
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Extract

In this paper we develop a descent technique for generalized (co)-homology theories defined in the category of algebraic varieties. By such a theory we mean a functor Sch→C, where C is a closed model category in the sense of Quillen satisfying certain axioms (cf. §4). We have chosen to work in such a general context so as to include two situations for which the results of SGA 4 of Deligne and Saint-Donat are not applicable: descent of multiplicative structures (i.e. of differential graded algebras) and descent for generalized sheaf cohomology (such as the algebraic K-theory of coherent sheaves over a noetherian scheme).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 100 , Issue 3 , November 1986 , pp. 459 - 474
Copyright
Copyright © Cambridge Philosophical Society 1986

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