Logarithmic Prismatic Cohomology via Logarithmic THH

Abstract

Inspired by Bhatt-Morrow-Scholze's work on $\mathrm{THH}$, we define Nygaard-completed log prismatic cohomology based on log topological Hochschild homology via filtrations on log $\mathrm{THH}$ and its variants. Moreover, of independent interest, we describe log $\mathrm{THH}$ for quasiregular semiperfectoids as a $1$-parameter deformation of ordinary, non-logarithmic Hochschild homology.

30 pages. Final version, with an additional comparison with log (derived) de Rham cohomology. To appear in IMRN