Volume: 314; 2007; 464 pp; Softcover
MSC: Primary 14; 18; 19;
Print ISBN: 978-2-85629-244-0
Product Code: AST/314
List Price: $132.00
AMS Member Price: $118.80
Les Six Opérations de Grothendieck et le Formalisme des Cycles Évanescents dans le Monde Motivique (I)
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A publication of the Société Mathématique de France
By the work of Morel, Voevodsky, and other mathematicians, one has the
notion of the stable motivic homotopy type of a
smooth \(S\)-scheme. This object lives in the stable homotopy
category of \(S\)-schemes SH\((S)\).
This work consists of two volumes and each of them is divided into
two chapters. In the first chapter, the author shows that from the
viewpoint of functoriality, the categories SH\((S)\)
behave like the derived categories of \(l\)-adic
sheaves. Indeed, the formalism of Grothendieck operations
\(f^*\), \(f_*\), \(f_!\) and \(f^!\)
extends to the motivic world. In the second chapter, the author
studies the constructibility of motives and develops Verdier
duality. The third chapter deals with the theory of nearby motives and
vanishing motives. The last chapter provides a self-contained
treatment of the construction of the categories
SH\((S)\).
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 algebra and algebraic geometry.