Logarithmic TC via the Infinite Root Stack and the Beilinson Fiber Square
arXiv:2408.15627
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 , and we establish a log version of the -variant of the Beilinson fiber square of Antieau--Mathew--Morrow--Nikolaus.
22 pages. Final version, to appear in Transactions of the AMS