**Astérisque**

Volume: 315;
2007;
362 pp;
Softcover

MSC: Primary 14; 18; 19;
**Print ISBN: 978-2-85629-245-7
Product Code: AST/315**

List Price: $117.00

Individual Member Price: $105.30

# Les Six Opérations de Grothendieck et le Formalisme des Cycles Évanescents dans le Monde Motivique (II)

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*Joseph Ayoub*

A publication of the Société Mathématique de France

This second volume contains chapters

This volume begins with the construction of the nearby motive functors \(\Psi _f\) which are the analogue of the nearby cycles functors, well-known in étale cohomology. The author then extends the vanishing cycles formalism to these functors. In particular, he computes the effect of the functor \(\Psi _f\) in the case where \(f\) has semi-stable reduction. He also shows that \(\Psi _f\) preserves constructible motives and commutes with external tensor product and duality. He then defines a monodromy operator and proves that this operator is nilpotent.

The last chapter, which is of a different nature than the previous ones, recalls in full detail the construction of the stable homotopy category of \(S\)-schemes.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

#### Readership

Graduate students and research mathematicians interested in number theory.