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

Fuente: arXiv
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Main Authors: Binda, Federico, Lundemo, Tommy, Merici, Alberto, Park, Doosung
Format: Preprint
Published: 2024
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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