Distribution algebras and arithmetic \(\mathcal{D}\)-modules
type: Item
instance of: scholarly article
title: Distribution algebras and arithmetic \(\mathcal{D}\)-modules
zbMATH Open document ID: 1485.14034
DOI: 10.4171/RSMUP/139-1
author: Tobias Schmidt
author: Christine Noot-Huyghe
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 2018-07-02T00:00:00Z
review text: Summary: Let \(p\) be a prime number, \(V\) a complete discrete valuation ring of unequal caracteristics \((0,p)\), \(G\) a smooth affine algebraic group over \(\operatorname{Spec} V\). Using partial divided powers techniques of Berthelot, we construct arithmetic distribution algebras, with level \(m\), generalizing the classical construction of the distribution algebra. We also construct the weak completion of the classical distribution algebra over a finite extension \(K\) of \(\mathbb{Q}_p\). We then show that these distribution algebras can be identified with invariant arithmetic differential operators over \(G\), and prove a coherence result when the ramification index of \(K\) is \(<p-1\).
Mathematics Subject Classification ID: 14F10
Mathematics Subject Classification ID: 14L15
Mathematics Subject Classification ID: 16S32
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G25
zbMATH DE Number: 6898039
zbMATH Keywords: arithmetic \(\mathcal{D}\)-modules
zbMATH Keywords: \(p\)-adic distribution algebras
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6898039