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Codescent theory II: Cofibrant approximations
, 2003
"... Abstract. We establish a general method to produce cofibrant approximations in the model category US(C, D) of Svalued Cindexed diagrams with Dweak equivalences and Dfibrations. We also present explicit examples of such approximations. Here, S is an arbitrary cofibrantly generated simplicial mode ..."
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Abstract. We establish a general method to produce cofibrant approximations in the model category US(C, D) of Svalued Cindexed diagrams with Dweak equivalences and Dfibrations. We also present explicit examples of such approximations. Here, S is an arbitrary cofibrantly generated simplicial model category and D ⊂ C are small categories. An application to the notion of homotopy colimit is presented. 1.
CODESCENT THEORY I: FOUNDATIONS
, 2003
"... C to S with a model structure, defining weak equivalences and fibrations objectwise but only on D. Our first concern is the effect of moving C, D and S. The main notion introduced here is the “Dcodescent ” property for objects in S C. Our longterm program aims at reformulating as codescent stateme ..."
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C to S with a model structure, defining weak equivalences and fibrations objectwise but only on D. Our first concern is the effect of moving C, D and S. The main notion introduced here is the “Dcodescent ” property for objects in S C. Our longterm program aims at reformulating as codescent statements the Conjectures of BaumConnes and FarrellJones, and at tackling them with new methods. Here, we set the grounds of a systematic theory of codescent, including pullbacks, pushforwards and various invariance properties. 1.
Lambda operations, K theory and motivic cohomology
"... This paper is in two parts: in part one, our main object is to give a construction of natural λoperations for relative Ktheory with supports, satisfying the special λring identities. In the second part, we give an application to the relation of motivic cohomology and algebraic Ktheory of a smoot ..."
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This paper is in two parts: in part one, our main object is to give a construction of natural λoperations for relative Ktheory with supports, satisfying the special λring identities. In the second part, we give an application to the relation of motivic cohomology and algebraic Ktheory of a smooth quasiprojective variety over a field.