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