Softcover ISBN:  9782856299395 
Product Code:  AST/425 
List Price:  $68.00 
AMS Member Price:  $54.40 
Softcover ISBN:  9782856299395 
Product Code:  AST/425 
List Price:  $68.00 
AMS Member Price:  $54.40 

Book DetailsAstérisqueVolume: 425; 2021; 208 ppMSC: Primary 14; 19
If \(f : S\prime \rightarrow S\) is a finite locally free morphism of schemes, the authors construct a symmetric monoidal “norm” functor \(f_{\otimes}:\mathcal{H}_{\bullet}(S\prime)\rightarrow \mathcal{H}_{\bullet}(S)\), where \(\mathcal{H}_{\bullet}(S)\) is the pointed unstable motivic homotopy category over \(S\). If \(f\) is finite étale, the authors show that it stabilizes to a functor \(f_{\otimes}:\mathcal{SH}(S\prime) \rightarrow\mathcal{SH}(S)\), where \(\mathcal{SH}(S)\) is the \(\mathbb{P}^{1}\)stable motivic homotopy category over \(S\).
Using these norm functors, the authors define the notion of a normed motivic spectrum, which is an enhancement of a motivic \(E_{\infty}\)ring spectrum. The main content of this text is a detailed study of the norm functors and of normed motivic spectra, and the construction of examples. In particular: the authors investigate the interaction of norms with Grothendieck's Galois theory, with Betti realization, and with Voevodsky's slice filtration; they prove that the norm functors categorify Rost's multiplicative transfers on GrothendieckWitt rings; and they construct normed spectrum structures on the motivic cohomology spectrum\(H\mathbb{Z}\), the homotopy \(K\)theory spectrum \(KGL\), and the algebraic cobordism spectrum \(MGL\). The normed spectrum structure on \(H\mathbb{Z}\) is a common refinement of Fulton and MacPherson's mutliplicative transfers on Chow groups and of Voevodsky's power operations in motivic cohomology.
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.
ReadershipGraduate students and research mathematicians.

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If \(f : S\prime \rightarrow S\) is a finite locally free morphism of schemes, the authors construct a symmetric monoidal “norm” functor \(f_{\otimes}:\mathcal{H}_{\bullet}(S\prime)\rightarrow \mathcal{H}_{\bullet}(S)\), where \(\mathcal{H}_{\bullet}(S)\) is the pointed unstable motivic homotopy category over \(S\). If \(f\) is finite étale, the authors show that it stabilizes to a functor \(f_{\otimes}:\mathcal{SH}(S\prime) \rightarrow\mathcal{SH}(S)\), where \(\mathcal{SH}(S)\) is the \(\mathbb{P}^{1}\)stable motivic homotopy category over \(S\).
Using these norm functors, the authors define the notion of a normed motivic spectrum, which is an enhancement of a motivic \(E_{\infty}\)ring spectrum. The main content of this text is a detailed study of the norm functors and of normed motivic spectra, and the construction of examples. In particular: the authors investigate the interaction of norms with Grothendieck's Galois theory, with Betti realization, and with Voevodsky's slice filtration; they prove that the norm functors categorify Rost's multiplicative transfers on GrothendieckWitt rings; and they construct normed spectrum structures on the motivic cohomology spectrum\(H\mathbb{Z}\), the homotopy \(K\)theory spectrum \(KGL\), and the algebraic cobordism spectrum \(MGL\). The normed spectrum structure on \(H\mathbb{Z}\) is a common refinement of Fulton and MacPherson's mutliplicative transfers on Chow groups and of Voevodsky's power operations in motivic cohomology.
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.
Graduate students and research mathematicians.