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A Commutative $\mathbb{ P}^1$-Spectrum Representing Motivic Cohomology Over Dedekind Domains
 
Markus Spitzweck Universität Osnabrück, Germany
A publication of the Société Mathématique de France
A Commutative P1-Spectrum Representing Motivic  Cohomology Over Dedekind Domains
Softcover ISBN:  978-2-85629-890-9
Product Code:  SMFMEM/157
List Price: $48.00
AMS Member Price: $38.40
Please note AMS points can not be used for this product
A Commutative P1-Spectrum Representing Motivic  Cohomology Over Dedekind Domains
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A Commutative $\mathbb{ P}^1$-Spectrum Representing Motivic Cohomology Over Dedekind Domains
Markus Spitzweck Universität Osnabrück, Germany
A publication of the Société Mathématique de France
Softcover ISBN:  978-2-85629-890-9
Product Code:  SMFMEM/157
List Price: $48.00
AMS Member Price: $38.40
Please note AMS points can not be used for this product
  • Book Details
     
     
    Mémoires de la Société Mathématique de France
    Volume: 1572018; 114 pp
    MSC: Primary 14; 19; 55

    The author constructs a motivic Eilenberg–Mac Lane spectrum with a highly structured multiplication over general base schemes which represents Levine's motivic cohomology, defined via Bloch's cycle complexes, over smooth schemes over Dedekind domains. The author's method involves gluing \(p\)-completed and rational parts along an arithmetic square. Hereby, the finite coefficient spectra are obtained by truncated étale sheaves (relying on the now proven Bloch-Kato conjecture) and a variant of Geisser's version of syntomic cohomology, and the rational spectra are the ones which represent Beilinson motivic cohomology.

    As an application, the arithmetic motivic cohomology groups can be realized as Ext-groups in a triangulated category of motives with integral coefficients. The author's spectrum is compatible with base change giving rise to a formalism of six functors for triangulated categories of motivic sheaves over general base schemes, including the localization triangle.

    Further applications are a generalization of the Hopkins-Morel isomorphism and a structure result for the dual motivic Steenrod algebra in the case where the coefficient characteristic is invertible on the base scheme.

    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.

  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 1572018; 114 pp
MSC: Primary 14; 19; 55

The author constructs a motivic Eilenberg–Mac Lane spectrum with a highly structured multiplication over general base schemes which represents Levine's motivic cohomology, defined via Bloch's cycle complexes, over smooth schemes over Dedekind domains. The author's method involves gluing \(p\)-completed and rational parts along an arithmetic square. Hereby, the finite coefficient spectra are obtained by truncated étale sheaves (relying on the now proven Bloch-Kato conjecture) and a variant of Geisser's version of syntomic cohomology, and the rational spectra are the ones which represent Beilinson motivic cohomology.

As an application, the arithmetic motivic cohomology groups can be realized as Ext-groups in a triangulated category of motives with integral coefficients. The author's spectrum is compatible with base change giving rise to a formalism of six functors for triangulated categories of motivic sheaves over general base schemes, including the localization triangle.

Further applications are a generalization of the Hopkins-Morel isomorphism and a structure result for the dual motivic Steenrod algebra in the case where the coefficient characteristic is invertible on the base scheme.

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.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.