Logarithmic TC via the Infinite Root Stack and the Beilinson Fiber Square
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.15627
- arXiv:
- arXiv:2408.15627
- Bibcode:
- 2024arXiv240815627B
- Keywords:
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- Mathematics - Algebraic Geometry;
- Mathematics - K-Theory and Homology;
- 14F30;
- 14A21;
- 14F40;
- 13D03
- E-Print:
- 20 pages, comments welcome!