Motivic and Étale Spanier-Whitehead duality and the Becker-Gottlieb transfer
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2020
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909175894769664 |
|---|---|
| author | Carlsson, Gunnar Joshua, Roy |
| author_facet | Carlsson, Gunnar Joshua, Roy |
| contents | In this paper, we develop a theory of Becker-Gottlieb transfer based on Spanier-Whitehead duality that holds in both the motivic and étale settings for smooth quasi-projective varieties in as broad a context as possible: for example, for varieties over non-separably closed fields in all characteristics, and also for both the étale and motivic settings.
In view of the fact that the most promising applications of the traditional Becker-Gottlieb transfer has been to torsors and Borel-style equivariant cohomology theories, we focus our applications to motivic cohomology theories for torsors as well as Borel-style equivariant motivic cohomology theories, both defined with respect to motivic spectra. We obtain several results in this direction, including a stable splitting in generalized motivic cohomology theories. Various further applications will be discussed in forthcoming papers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_02247 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Motivic and Étale Spanier-Whitehead duality and the Becker-Gottlieb transfer Carlsson, Gunnar Joshua, Roy Algebraic Geometry 14F20, 14F42, 14L30 In this paper, we develop a theory of Becker-Gottlieb transfer based on Spanier-Whitehead duality that holds in both the motivic and étale settings for smooth quasi-projective varieties in as broad a context as possible: for example, for varieties over non-separably closed fields in all characteristics, and also for both the étale and motivic settings. In view of the fact that the most promising applications of the traditional Becker-Gottlieb transfer has been to torsors and Borel-style equivariant cohomology theories, we focus our applications to motivic cohomology theories for torsors as well as Borel-style equivariant motivic cohomology theories, both defined with respect to motivic spectra. We obtain several results in this direction, including a stable splitting in generalized motivic cohomology theories. Various further applications will be discussed in forthcoming papers. |
| title | Motivic and Étale Spanier-Whitehead duality and the Becker-Gottlieb transfer |
| topic | Algebraic Geometry 14F20, 14F42, 14L30 |
| url | https://arxiv.org/abs/2007.02247 |