Relative cyclotomic structures and equivariant complex cobordism
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866917876945911808 |
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| author | Blumberg, Andrew J. Mandell, Michael A. Yuan, Allen |
| author_facet | Blumberg, Andrew J. Mandell, Michael A. Yuan, Allen |
| contents | We describe a structure on a commutative ring (pre)cyclotomic spectrum $R$ that gives rise to a (pre)cyclotomic structure on topological Hochschild homology ($THH$) relative to its underlying commutative ring spectrum. This lets us construct $TC$ relative to $R$, denoted $TC^{R}$, and we prove some descent results relating $TC^{R}$ and $TC$. We explore several examples of this structure on familiar $\mathbb{T}$-equivariant commutative ring spectra including the periodic $\mathbb{T}$-equivariant complex cobordism spectrum $MUP_{\mathbb{T}}$ and a new (connective) equivariant version of the complex cobordism spectrum $MU$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_02348 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Relative cyclotomic structures and equivariant complex cobordism Blumberg, Andrew J. Mandell, Michael A. Yuan, Allen Algebraic Topology K-Theory and Homology Primary 19D10, Secondary 55P60 We describe a structure on a commutative ring (pre)cyclotomic spectrum $R$ that gives rise to a (pre)cyclotomic structure on topological Hochschild homology ($THH$) relative to its underlying commutative ring spectrum. This lets us construct $TC$ relative to $R$, denoted $TC^{R}$, and we prove some descent results relating $TC^{R}$ and $TC$. We explore several examples of this structure on familiar $\mathbb{T}$-equivariant commutative ring spectra including the periodic $\mathbb{T}$-equivariant complex cobordism spectrum $MUP_{\mathbb{T}}$ and a new (connective) equivariant version of the complex cobordism spectrum $MU$. |
| title | Relative cyclotomic structures and equivariant complex cobordism |
| topic | Algebraic Topology K-Theory and Homology Primary 19D10, Secondary 55P60 |
| url | https://arxiv.org/abs/2310.02348 |