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arXiv · 2408.15627

Logarithmic TC via the Infinite Root Stack and the Beilinson Fiber Square

Federico Binda·Tommy Lundemo·Alberto Merici·Doosung Park
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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.

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Federico Binda, Tommy Lundemo, Alberto Merici, Doosung Park. 2024-08-28. Logarithmic TC via the Infinite Root Stack and the Beilinson Fiber Square. https://arxiv.org/abs/2408.15627

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