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Motifs des variétés analytiques rigides


Ayoub, Joseph (2015). Motifs des variétés analytiques rigides. Paris: Société Mathematique de France.

Abstract

In this work, I extend the theory of motives, as developed by Voevodsky and Morel-Voevodsky, to the context of rigid analytic geometry over a complete non archimedean field. The first chapter deals with the homotopical approach of Morel and Voevodsky. One finds there the construction of the motivic stable homotopy category of rigid analytic varieties and a complete description of this category in terms of algebraic motives when the base field has equal characteristic zero and its valuation is discrete. The second chapter deals with Voevodsky's approach based on transfers. One finds there the construction of the triangulated category of rigid analytic motives, and an extension to rigid analytic geometry of a large number of Voevodsky's fundamental results such as his theory of homotopy invariants presheaves with transfers. This is said, the present work is a lot more than just a mere copy of the classical theory and the reader will find a lot of results that are new and specific to rigid analytic geometry.

In this work, I extend the theory of motives, as developed by Voevodsky and Morel-Voevodsky, to the context of rigid analytic geometry over a complete non archimedean field. The first chapter deals with the homotopical approach of Morel and Voevodsky. One finds there the construction of the motivic stable homotopy category of rigid analytic varieties and a complete description of this category in terms of algebraic motives when the base field has equal characteristic zero and its valuation is discrete. The second chapter deals with Voevodsky's approach based on transfers. One finds there the construction of the triangulated category of rigid analytic motives, and an extension to rigid analytic geometry of a large number of Voevodsky's fundamental results such as his theory of homotopy invariants presheaves with transfers. This is said, the present work is a lot more than just a mere copy of the classical theory and the reader will find a lot of results that are new and specific to rigid analytic geometry.

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Additional indexing

Other titles:Motives of rigid analytic varieties
Item Type:Monograph
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:French
Date:2015
Deposited On:27 Jan 2016 11:02
Last Modified:27 Oct 2016 07:11
Publisher:Société Mathematique de France
Series Name:Mémoires de la SMF. Nouvelle Série/Supplement
Volume:140-141
Number of Pages:386
ISSN:0249-633X
ISBN:978-2-85629-811-4
Official URL:http://smf4.emath.fr/en/Publications/Memoires/2015/140-141/html/smf_mem-ns_140-141.php
Related URLs:http://www.recherche-portal.ch/ZAD:default_scope:ebi01_prod010474060 (Library Catalogue)

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