Cyclotomic synthetic spectra
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917852249849856 |
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| author | Antieau, Benjamin Riggenbach, Noah |
| author_facet | Antieau, Benjamin Riggenbach, Noah |
| contents | We define an $\infty$-category $\mathrm{CycSyn}$ of $p$-typical cyclotomic synthetic spectra and prove that the motivic filtration on $\mathrm{THH}(R;\mathbf{Z}_p)$, defined by Bhatt, Morrow, and Scholze when $R$ is quasisyntomic and by Hahn, Raksit, and Wilson in the chromatically quasisyntomic case, naturally admits the structure of a $p$-typical cyclotomic synthetic spectrum. As a consequence, we obtain new bounds on the syntomic cohomology of connective chromatically quasisyntomic $\mathbf{E}_\infty$-ring spectra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19929 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cyclotomic synthetic spectra Antieau, Benjamin Riggenbach, Noah K-Theory and Homology Algebraic Geometry Algebraic Topology We define an $\infty$-category $\mathrm{CycSyn}$ of $p$-typical cyclotomic synthetic spectra and prove that the motivic filtration on $\mathrm{THH}(R;\mathbf{Z}_p)$, defined by Bhatt, Morrow, and Scholze when $R$ is quasisyntomic and by Hahn, Raksit, and Wilson in the chromatically quasisyntomic case, naturally admits the structure of a $p$-typical cyclotomic synthetic spectrum. As a consequence, we obtain new bounds on the syntomic cohomology of connective chromatically quasisyntomic $\mathbf{E}_\infty$-ring spectra. |
| title | Cyclotomic synthetic spectra |
| topic | K-Theory and Homology Algebraic Geometry Algebraic Topology |
| url | https://arxiv.org/abs/2411.19929 |