A1-algebraic topology over a field
This text deals with A<sup>1</sup>-homotopy theory over a base field, i.e., with the natural homotopy theory associated to the category of smooth varieties over a field in which the affine line is imposed to be contractible. It is a natural sequel to the foundational paper on A<sup>...
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Auteur principal : | |
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Format : | Livre |
Langue : | anglais |
Titre complet : | A1-algebraic topology over a field / Fabien Morel |
Édition : | 1st ed. 2012. |
Publié : |
Berlin, Heidelberg :
Springer Berlin Heidelberg
, [20..] Cham : Springer Nature |
Collection : | Lecture notes in mathematics (Internet) ; 2052 |
Accès en ligne : |
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Condition d'utilisation et de reproduction : | Conditions particulières de réutilisation pour les bénéficiaires des licences nationales : https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |
Contenu : | 1 Introduction. 2 Unramified sheaves and strongly A1-invariant sheaves. 3 Unramified Milnor-Witt K-theories. 4 Geometric versus canonical transfers. 5 The Rost-Schmid complex of a strongly A1-invariant sheaf. 6 A1-homotopy sheaves and A1-homology sheaves. 7 A1-coverings. 8 A1-homotopy and algebraic vector bundles. 9 The affine B.G. property for the linear groups and the Grassmanian |
Sujets : | |
Documents associés : | Autre format:
A1-algebraic topology over a field Autre format: A1-algebraic topology over a field Autre format: A1-Algebraic Topology over a Field |
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205 | |a 1st ed. 2012. | ||
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225 | 2 | |a Lecture notes in mathematics |x 1617-9692 |v 2052 | |
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327 | 1 | |a 1 Introduction |a 2 Unramified sheaves and strongly A1-invariant sheaves |a 3 Unramified Milnor-Witt K-theories |a 4 Geometric versus canonical transfers |a 5 The Rost-Schmid complex of a strongly A1-invariant sheaf |a 6 A1-homotopy sheaves and A1-homology sheaves |a 7 A1-coverings |a 8 A1-homotopy and algebraic vector bundles |a 9 The affine B.G. property for the linear groups and the Grassmanian | |
330 | |a This text deals with A<sup>1</sup>-homotopy theory over a base field, i.e., with the natural homotopy theory associated to the category of smooth varieties over a field in which the affine line is imposed to be contractible. It is a natural sequel to the foundational paper on A<sup>1</sup>-homotopy theory written together with V. Voevodsky. Inspired by classical results in algebraic topology, we present new techniques, new results and applications related to the properties and computations of A<sup>1</sup>-homotopy sheaves, A<sup>1</sup>-homotogy sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties | ||
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