Logarithmic TC via the Infinite Root Stack and the Beilinson Fiber Square. arXiv:2408.15627
Preprint, arXiv:2408.15627 [math.AG] (2024).
Summary: 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.
MSC:
| 14F30 | \(p\)-adic cohomology, crystalline cohomology |
| 14A21 | Logarithmic algebraic geometry, log schemes |
| 14F40 | de Rham cohomology and algebraic geometry |
| 13D03 | (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) |
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