# Les six opérations de Grothendieck et le formalisme des cycles évanescentes dans le monde motivique I, II

These two volumes, each consisting of two long chapters, represent an important contribution to stable motivic homotopy theory. In chapter 1, the author constructs the Grothendieck four functors f*, f*, f! and f! in this context (this result was earlier announced by Voevodsky but the details of his construction are still being awaited). Chapter 2 is devoted to constructability properties of these functors and the Verdier duality. In chapter 3, the author develops a motivic formalism of nearby and vanishing cycles. Chapter 4 sums up a construction of the stable homotopy category over a given scheme. Both volumes are written very clearly and carefully. They also include a substantial amount of abstract background material used by the author (e.g. 2-categories, properties of triangulated categories, derivators and homotopical algebra).

Reviewer:
jnek
Book details
Author:  Publisher:
Published:
2007
ISBN:
978-2-85629-245-7
Price:
EUR 78
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