| Author: | Fabien Morel | ISBN: | 9783642295140 |
| Publisher: | Springer Berlin Heidelberg | Publication: | July 13, 2012 |
| Imprint: | Springer | Language: | English |
| Author: | Fabien Morel |
| ISBN: | 9783642295140 |
| Publisher: | Springer Berlin Heidelberg |
| Publication: | July 13, 2012 |
| Imprint: | Springer |
| Language: | English |
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.
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.
