Etale cohomology of diamonds
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2017
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866908960620019712 |
|---|---|
| author | Scholze, Peter |
| author_facet | Scholze, Peter |
| contents | Motivated by problems on the étale cohomology of Rapoport--Zink spaces and their generalizations, as well as Fargues's geometrization conjecture for the local Langlands correspondence, we develop a six functor formalism for the étale cohomology of diamonds, and more generally small v-stacks on the category of perfectoid spaces of characteristic $p$. Using a natural functor from analytic adic spaces over $\mathbb Z_p$ to diamonds which identifies étale sites, this induces a similar formalism in that setting, which in the noetherian setting recovers the formalism from Huber's book. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1709_07343 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Etale cohomology of diamonds Scholze, Peter Algebraic Geometry Number Theory 14F20, 14F05, 14G22, 14G20 Motivated by problems on the étale cohomology of Rapoport--Zink spaces and their generalizations, as well as Fargues's geometrization conjecture for the local Langlands correspondence, we develop a six functor formalism for the étale cohomology of diamonds, and more generally small v-stacks on the category of perfectoid spaces of characteristic $p$. Using a natural functor from analytic adic spaces over $\mathbb Z_p$ to diamonds which identifies étale sites, this induces a similar formalism in that setting, which in the noetherian setting recovers the formalism from Huber's book. |
| title | Etale cohomology of diamonds |
| topic | Algebraic Geometry Number Theory 14F20, 14F05, 14G22, 14G20 |
| url | https://arxiv.org/abs/1709.07343 |