Operations on Milnor-Witt K-theory
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866917935633661952 |
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| author | Wittich, Thor |
| author_facet | Wittich, Thor |
| contents | For all positive integers $n$ and all homotopy modules $M_*$, we define certain operations $\underline{\operatorname{K}}^{\operatorname{MW}}_n \rightarrow M_*$ and show that these generate the $M_*(k)$-module of all (in general non-additive) operations $\underline{\operatorname{K}}^{\operatorname{MW}}_n \rightarrow M_*$ in a suitable sense, if $M_*$ is $\mathbb{N}$-graded and has a ring structure. This also allows us to explicitly compute the abelian group $\operatorname{Op}(\underline{\operatorname{K}}^{\operatorname{MW}}_n,\underline{\operatorname{K}}^{\operatorname{MW}}_m)$ and all operations between related theories such as Milnor, Witt and Milnor-Witt K-theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_01008 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Operations on Milnor-Witt K-theory Wittich, Thor Algebraic Topology Algebraic Geometry K-Theory and Homology 19D45 (Primary) 14F42, 55Q35, 55Q45, 55S25 (Secondary) For all positive integers $n$ and all homotopy modules $M_*$, we define certain operations $\underline{\operatorname{K}}^{\operatorname{MW}}_n \rightarrow M_*$ and show that these generate the $M_*(k)$-module of all (in general non-additive) operations $\underline{\operatorname{K}}^{\operatorname{MW}}_n \rightarrow M_*$ in a suitable sense, if $M_*$ is $\mathbb{N}$-graded and has a ring structure. This also allows us to explicitly compute the abelian group $\operatorname{Op}(\underline{\operatorname{K}}^{\operatorname{MW}}_n,\underline{\operatorname{K}}^{\operatorname{MW}}_m)$ and all operations between related theories such as Milnor, Witt and Milnor-Witt K-theory. |
| title | Operations on Milnor-Witt K-theory |
| topic | Algebraic Topology Algebraic Geometry K-Theory and Homology 19D45 (Primary) 14F42, 55Q35, 55Q45, 55S25 (Secondary) |
| url | https://arxiv.org/abs/2308.01008 |