Commuting unbounded homotopy limits with Morava K-theory
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866912416180207616 |
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| author | Angelini-Knoll, Gabriel Salch, Andrew |
| author_facet | Angelini-Knoll, Gabriel Salch, Andrew |
| contents | This paper provides conditions for Morava $K$-theory to commute with certain homotopy limits. These conditions extend previous work on this question by allowing for homotopy limits of sequences of spectra that are not uniformly bounded below. As an application, we prove the $K(n)$-local triviality (for sufficiently large $n$) of the algebraic $K$-theory of algebras over truncated Brown--Peterson spectra, building on work of Bruner--Rognes and extending a classical theorem of Mitchell on $K(n)$-local triviality of the algebraic K-theory spectrum of the integers for large enough $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_03510 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Commuting unbounded homotopy limits with Morava K-theory Angelini-Knoll, Gabriel Salch, Andrew Algebraic Topology K-Theory and Homology 55P42, 19D55 This paper provides conditions for Morava $K$-theory to commute with certain homotopy limits. These conditions extend previous work on this question by allowing for homotopy limits of sequences of spectra that are not uniformly bounded below. As an application, we prove the $K(n)$-local triviality (for sufficiently large $n$) of the algebraic $K$-theory of algebras over truncated Brown--Peterson spectra, building on work of Bruner--Rognes and extending a classical theorem of Mitchell on $K(n)$-local triviality of the algebraic K-theory spectrum of the integers for large enough $n$. |
| title | Commuting unbounded homotopy limits with Morava K-theory |
| topic | Algebraic Topology K-Theory and Homology 55P42, 19D55 |
| url | https://arxiv.org/abs/2003.03510 |