Logarithmic Prismatic Cohomology via Logarithmic THH

Author:

Federico Binda, Tommy Lundemo, Doosung Park, Paul Arne Østvær

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), K-Theory and Homology (math.KT)

journal:

date:

2023-06-01 16:00:00

Abstract

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

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