Inspired by Bhatt–Morrow–Scholze’s work on THH, we define Nygaard-completed log prismatic cohomology based on log topological Hochschild homology via filtrations on log THH and its variants. Moreover, of independent interest, we describe log THH for quasiregular semiperfectoid pre-log rings as a 1-parameter deformation of ordinary, non-logarithmic Hochschild homology
Logarithmic Prismatic Cohomology via Logarithmic THH / F. Binda, T. Lundemo, D. Park, P.A. Oestvaer. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - 2023:22(2023 Nov), pp. 19641-19696. [10.1093/imrn/rnad224]
Logarithmic Prismatic Cohomology via Logarithmic THH
F. Binda
Primo
;P.A. OestvaerUltimo
2023
Abstract
Inspired by Bhatt–Morrow–Scholze’s work on THH, we define Nygaard-completed log prismatic cohomology based on log topological Hochschild homology via filtrations on log THH and its variants. Moreover, of independent interest, we describe log THH for quasiregular semiperfectoid pre-log rings as a 1-parameter deformation of ordinary, non-logarithmic Hochschild homology
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