Strongly A^1-invariant sheaves (after F. Morel)
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911920625287168 |
|---|---|
| author | Bachmann, Tom |
| author_facet | Bachmann, Tom |
| contents | Strongly (respectively strictly) A1-invariant sheaves are foundational for motivic homotopy theory over fields. They are sheaves of (abelian) groups on the Nisnevich site of smooth varieties over a field k, with the property that their zeroth and first Nisnevich cohomology sets (respectively all Nisnevich cohomology groups) are invariant under replacing a variety X by the affine line over X. A celebrated theorem of Fabien Morel states that if the base field k is perfect, then any strongly A1-invariant sheaf of abelian groups is automatically strictly A1-invariant.
The aim of these lecture notes is twofold: (1) provide a complete proof if this result, and (2) outline some of its applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11526 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strongly A^1-invariant sheaves (after F. Morel) Bachmann, Tom Algebraic Geometry Algebraic Topology K-Theory and Homology Strongly (respectively strictly) A1-invariant sheaves are foundational for motivic homotopy theory over fields. They are sheaves of (abelian) groups on the Nisnevich site of smooth varieties over a field k, with the property that their zeroth and first Nisnevich cohomology sets (respectively all Nisnevich cohomology groups) are invariant under replacing a variety X by the affine line over X. A celebrated theorem of Fabien Morel states that if the base field k is perfect, then any strongly A1-invariant sheaf of abelian groups is automatically strictly A1-invariant. The aim of these lecture notes is twofold: (1) provide a complete proof if this result, and (2) outline some of its applications. |
| title | Strongly A^1-invariant sheaves (after F. Morel) |
| topic | Algebraic Geometry Algebraic Topology K-Theory and Homology |
| url | https://arxiv.org/abs/2406.11526 |