Logarithmic TC via the Infinite Root Stack and the Beilinson Fiber Square
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912673010024448 |
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| author | Binda, Federico Lundemo, Tommy Merici, Alberto Park, Doosung |
| author_facet | Binda, Federico Lundemo, Tommy Merici, Alberto Park, Doosung |
| contents | We apply our previous results on ``saturated descent'' to express a wide range of logarithmic cohomology theories in terms of the infinite root stack. Examples include the log cotangent complex, Rognes' log topological cyclic homology, and Nygaard-complete log prismatic cohomology. As applications, we show that the Nygaard-completion of the site-theoretic log prismatic cohomology coincides with the definition arising from log ${\rm TC}$, and we establish a log version of the ${\rm TC}$-variant of the Beilinson fiber square of Antieau--Mathew--Morrow--Nikolaus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15627 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Logarithmic TC via the Infinite Root Stack and the Beilinson Fiber Square Binda, Federico Lundemo, Tommy Merici, Alberto Park, Doosung Algebraic Geometry K-Theory and Homology 14F30, 14A21, 14F40, 13D03 We apply our previous results on ``saturated descent'' to express a wide range of logarithmic cohomology theories in terms of the infinite root stack. Examples include the log cotangent complex, Rognes' log topological cyclic homology, and Nygaard-complete log prismatic cohomology. As applications, we show that the Nygaard-completion of the site-theoretic log prismatic cohomology coincides with the definition arising from log ${\rm TC}$, and we establish a log version of the ${\rm TC}$-variant of the Beilinson fiber square of Antieau--Mathew--Morrow--Nikolaus. |
| title | Logarithmic TC via the Infinite Root Stack and the Beilinson Fiber Square |
| topic | Algebraic Geometry K-Theory and Homology 14F30, 14A21, 14F40, 13D03 |
| url | https://arxiv.org/abs/2408.15627 |