# Topological Hochschild homology and Zeta-values

@article{Morin2020TopologicalHH, title={Topological Hochschild homology and Zeta-values}, author={Baptiste Morin}, journal={arXiv: Number Theory}, year={2020} }

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

### A motivic filtration on the topological cyclic homology of commutative ring spectra

- 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…

### Zeta-values of one-dimensional arithmetic schemes at strictly negative integers

- Mathematics
- 2021

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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