Modules over motivic cohomology

Autor(en): Roendings, Oliver
Ostvaer, Paul Arne
Stichwörter: ALGEBRAIC VARIETY; FIELD; Mathematics; MODEL CATEGORIES; motives; motivic homotopy theory; RESOLUTION; SINGULARITIES
Erscheinungsdatum: 2008
Herausgeber: ACADEMIC PRESS INC ELSEVIER SCIENCE
Journal: ADVANCES IN MATHEMATICS
Volumen: 219
Ausgabe: 2
Startseite: 689
Seitenende: 727
Zusammenfassung: 
For fields of characteristic zero, we show that the homotopy category of modules over the motivic ring spectrum representing motivic cohomology is equivalent to Voevodsky's big category of motives. ne proof makes use of some highly structured models for motivic stable homotopy theory, motivic Spanier-Whitehead duality, the homotopy theories of motivic functors and of motivic spaces with transfers as introduced from ground up in this paper. Working with rational coefficients, we extend the equivalence for fields of characteristic zero to all perfect fields by employing the techniques of alterations and homotopy purity in motivic homotopy theory. (C) 2008 Elsevier Inc. All rights reserved.
ISSN: 00018708
DOI: 10.1016/j.aim.2008.05.013

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