Logarithmic Prismatic Cohomology via Logarithmic THH

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

Logarithmic Prismatic Cohomology via Logarithmic THH

Algebraic Geometry 2023-09-07 v2 K-Theory and Homology

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

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.

Keywords

logarithmic prismatic cohomology log thh nygaard completion quasiregular semiperfectoids hochschild homology filtrations

Cite

@article{arxiv.2306.01368,
  title  = {Logarithmic Prismatic Cohomology via Logarithmic THH},
  author = {Federico Binda and Tommy Lundemo and Doosung Park and Paul Arne Østvær},
  journal= {arXiv preprint arXiv:2306.01368},
  year   = {2023}
}

Comments

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

Logarithmic Prismatic Cohomology via Logarithmic THH

Abstract

Keywords

Cite

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