On the Balmer spectrum of the Morel-Voevodsky category
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909271167336448 |
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| author | Du, Peng Vishik, Alexander |
| author_facet | Du, Peng Vishik, Alexander |
| contents | We introduce the Morava-isotropic stable homotopy category and, more generally, the stable homotopy category of an extension $E/k$. These "local" versions of the Morel-Voevodsky stable ${\Bbb{A}}^1$-homotopy category $SH(k)$ are analogues of local motivic categories introduced in [22], but with a substantially more general notion of "isotropy". This permits to construct the, so-called, isotropic Morava points of the Balmer spectrum $\operatorname{Spc}(SH^c(k))$ of (the compact part of) the Morel-Voevodsky category. These analogues of topological Morava points are parametrized by the choice of Morava K-theory and a $K(p,m)$-equivalence class of extensions $E/k$. This provides a large supply of new points, and substantially improves our understanding of the spectrum. An interesting new feature is that the specialization among isotropic points behaves differently than in topology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09077 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Balmer spectrum of the Morel-Voevodsky category Du, Peng Vishik, Alexander Algebraic Geometry Algebraic Topology K-Theory and Homology 14F42 We introduce the Morava-isotropic stable homotopy category and, more generally, the stable homotopy category of an extension $E/k$. These "local" versions of the Morel-Voevodsky stable ${\Bbb{A}}^1$-homotopy category $SH(k)$ are analogues of local motivic categories introduced in [22], but with a substantially more general notion of "isotropy". This permits to construct the, so-called, isotropic Morava points of the Balmer spectrum $\operatorname{Spc}(SH^c(k))$ of (the compact part of) the Morel-Voevodsky category. These analogues of topological Morava points are parametrized by the choice of Morava K-theory and a $K(p,m)$-equivalence class of extensions $E/k$. This provides a large supply of new points, and substantially improves our understanding of the spectrum. An interesting new feature is that the specialization among isotropic points behaves differently than in topology. |
| title | On the Balmer spectrum of the Morel-Voevodsky category |
| topic | Algebraic Geometry Algebraic Topology K-Theory and Homology 14F42 |
| url | https://arxiv.org/abs/2309.09077 |