A1-Algebraic Topology over a Field
- ISBN-10
- 3642295142
- ISBN-13
- 9783642295140
- Category
- Mathematics
- Pages
- 259
- Language
- English
- Published
- 2012-07-13
- Publisher
- Springer
- Author
- Fabien Morel
Description
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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