TOPOLOGICAL HOCHSCHILD HOMOLOGY AND ZETA-VALUES
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | MORIN, Baptiste | |
| dc.date.accessioned | 2024-04-04T02:32:44Z | |
| dc.date.available | 2024-04-04T02:32:44Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190407 | |
| dc.description.abstractEn | Using work of Antieau and Bhatt-Morrow-Scholze, we define a filtration on topological Hochschild homology and its variants TP and TC^- of quasi-lci rings with bounded torsion, which recovers the BMS-filtration after p-adic completion. Then we compute the graded pieces of this filtration in terms of Hodge completed derived de Rham cohomology relative to the base ring Z. We denote the cofiber of the canonical map from gr^n TC^-(-) to gr^nTP(-) by LΩ^{<n}_{−/S}[2n]. Let X be a regular connected scheme of dimension d proper over Spec(Z) and let n∈Z be an arbitrary integer. Together with Weil-étale cohomology with compact support RΓ_{W,c}(X , Z(n)), the complex LΩ^{<n}_{X /S} is expected to give the Zeta-value ±ζ^*(X,n) on the nose. Combining the results proven here with a theorem recently proven in joint work with Flach, we obtain a formula relating LΩ^{<n}_{X /S}, LΩ^{<d-n}_{X/S}, Weil-étale cohomology of the archimedean fiber X_{\infty} with Tate twists n and d-n, the Bloch conductor A(X) and the special values of the archimedean Euler factor of the Zeta-function ζ(X,s) at s=n and s=d-n. This formula is a shadow of the functional equation of Zeta-functions. | |
| dc.language.iso | en | |
| dc.subject.en | de Rham cohomology | |
| dc.subject.en | 2010 Mathematics Subject Classification. 11G40 | |
| dc.subject.en | 14G10 | |
| dc.subject.en | 14F40 | |
| dc.subject.en | 14F42 | |
| dc.subject.en | 13D03 Arithmetic schemes | |
| dc.subject.en | Zeta-values | |
| dc.subject.en | Functional equation | |
| dc.subject.en | Topological Hochschild homology | |
| dc.title.en | TOPOLOGICAL HOCHSCHILD HOMOLOGY AND ZETA-VALUES | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math] | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-03429142 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03429142v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=MORIN,%20Baptiste&rft.genre=preprint |
Fichier(s) constituant ce document
| Fichiers | Taille | Format | Vue |
|---|---|---|---|
|
Il n'y a pas de fichiers associés à ce document. |
|||