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Record Nr. |
UNINA9910484007003321 |
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Autore |
Morel Fabien |
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Titolo |
A1-algebraic topology over a field / / Fabien Morel |
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Pubbl/distr/stampa |
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Berlin ; ; Heidelberg, : Springer, c2012 |
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ISBN |
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Edizione |
[1st ed. 2012.] |
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Descrizione fisica |
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1 online resource (X, 259 p.) |
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Collana |
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Lecture notes in mathematics ; ; 2052 |
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Disciplina |
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Soggetti |
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Algebraic topology |
Homotopy theory |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references (p. 255-258) and index. |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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This text deals with A1-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 A1-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 A1-homotopy sheaves, A1-homology sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties. |
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