Unstable $p$-completion in motivic homotopy theory
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_ | 1866929230687764480 |
|---|---|
| author | Mattis, Klaus |
| author_facet | Mattis, Klaus |
| contents | We define unstable $p$-completion in general $\infty$-topoi and the unstable motivic homotopy category, and prove that the $p$-completion of a nilpotent sheaf or motivic space can be computed on its Postnikov tower. We then show that the ($p$-completed) homotopy groups of the $p$-completion of a nilpotent motivic space $X$ fit into short exact sequences $0 \to \mathbb L_0 π_n(X) \to π_n^p(X_p^\wedge) \to \mathbb L_1 π_{n-1}(X) \to 0$, where the $\mathbb L_i$ are (versions of) the derived $p$-completion functors, analogous to the classical situation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17848 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unstable $p$-completion in motivic homotopy theory Mattis, Klaus Algebraic Geometry Algebraic Topology We define unstable $p$-completion in general $\infty$-topoi and the unstable motivic homotopy category, and prove that the $p$-completion of a nilpotent sheaf or motivic space can be computed on its Postnikov tower. We then show that the ($p$-completed) homotopy groups of the $p$-completion of a nilpotent motivic space $X$ fit into short exact sequences $0 \to \mathbb L_0 π_n(X) \to π_n^p(X_p^\wedge) \to \mathbb L_1 π_{n-1}(X) \to 0$, where the $\mathbb L_i$ are (versions of) the derived $p$-completion functors, analogous to the classical situation. |
| title | Unstable $p$-completion in motivic homotopy theory |
| topic | Algebraic Geometry Algebraic Topology |
| url | https://arxiv.org/abs/2401.17848 |