MORIN, Baptiste

Métadonnées

Afficher la notice complète

Licence d’utilisation du document

MORIN, Baptiste
Institut de Mathématiques de Bordeaux [IMB]

Langue

Document de travail - Pré-publication

Résumé en anglais

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.< Réduire

Mots clés en anglais

de Rham cohomology

2010 Mathematics Subject Classification. 11G40

14G10

14F40

14F42

13D03 Arithmetic schemes

Zeta-values

Functional equation

Topological Hochschild homology

Métadonnées

Partager cette publication !

Licence d’utilisation du document

TOPOLOGICAL HOCHSCHILD HOMOLOGY AND ZETA-VALUES

Langue

Résumé en anglais

Mots clés en anglais

URI

Origine

Unités de recherche