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 T C \mathrm {TC} , and we establish a log version of the T C \mathrm {TC} -variant of the Beilinson fiber square of Antieau–Mathew–Morrow–Nikolaus.
Fields of Study & Subjects
Matrix Theory and Algorithms
Publication details
- Journal / source
- Transactions of the American Mathematical Society
- Volume
- 379
- Issue
- 9
- Pages
- 6565–6588
- Publication date
- 8 May 2026
- Language
- EN