• Corpus ID: 227127688

# Topological Hochschild homology and Zeta-values

@article{Morin2020TopologicalHH,
title={Topological Hochschild homology and Zeta-values},
author={Baptiste Morin},
journal={arXiv: Number Theory},
year={2020}
}
• B. Morin
• Published 23 November 2020
• Mathematics
• arXiv: Number Theory
Using work of Antieau and Bhatt-Morrow-Scholze, we define a filtration on topological Hochschild homology and its variants of quasi-lci schemes with bounded torsion. Then we compute the graded pieces of this filtration in terms of Hodge completed derived de Rham cohomology relative to the base ring $\mathbb{Z}$. We denote the cofiber of the canonical map from $\mathrm{gr}^{n}TC^-(-)$ to $\mathrm{gr}^{n}TP(-)$ by $L\Omega^{<n}_{-/\mathbb{S}}[2n]$. Let $\mathcal{X}$ be a regular connected scheme…
2 Citations
• Mathematics
• 2022
. For a prime number 𝑝 and a 𝑝 -quasisyntomic commutative ring 𝑅 , Bhatt–Morrow–Scholze deﬁned motivic ﬁltrations on the 𝑝 -completions of THH , and TC , with the associated graded objects for TP
Let X be an arithmetic scheme (i.e., separated, of finite type over SpecZ) of Krull dimension 1. For the associated zeta function ζ(X, s), we write down a formula for the special value at s = n < 0

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