On the Geometry of Global Function Fields, the Riemann–Roch Theorem, and Finiteness Properties of S-Arithmetic Groups
type: Item
instance of: scholarly article
title: On the Geometry of Global Function Fields, the Riemann–Roch Theorem, and Finiteness Properties of S-Arithmetic Groups
zbMATH Open document ID: 1270.11056
DOI: 10.1007/978-1-4614-0709-6_4
published in: Buildings, Finite Geometries and Groups
publication date: 2012-09-28T00:00:00Z
full work available at URL: https://arxiv.org/abs/1008.3664
Mathematics Subject Classification ID: 11F75
Mathematics Subject Classification ID: 22E40
Mathematics Subject Classification ID: 51E24
zbMATH DE Number: 6087792
zbMATH Keywords: \(S\)-arithmetic groups over global function fields
zbMATH Keywords: reduction theory
zbMATH Keywords: Bruhat-Tits buildings
zbMATH Keywords: finiteness properties
zbMATH Keywords: isoperimetric properties
author: Ralf Köhl (né Gramlich)
MaRDI profile type: Publication
OpenAlex ID: W3145726815
arXiv ID: 1008.3664
cites work: Buildings
cites work: Twin buildings and applications to \(S\)-arithmetic groups
cites work: Algebraic functions and analogue of the geometry of numbers: The Riemann- Roch theorem
cites work: Axiomatic characterization of fields by the product formula for valuations
cites work: Arithmetic groups over function fields I
cites work: Q4664536
cites work: Higher finiteness properties of reductive arithmetic groups in positive characteristic: the rank theorem.
cites work: Arithmetic subgroups of algebraic groups
cites work: Q4720067
cites work: Q3999894
cites work: Finiteness properties of groups
cites work: Cohomologie d'immeubles et de groupes S-arithmétiques
cites work: Finiteness properties of arithmetic groups over function fields.
cites work: Connectivity properties of horospheres in Euclidean buildings and applications to finiteness properties of discrete groups.
cites work: Q5810622
cites work: Q2543784
cites work: Q4317713
cites work: Sur La Classification Des Fibres Holomorphes Sur La Sphere de Riemann
cites work: Éléments de géométrie algébrique. I: Le langage des schémas. II: Étude globale élémentaire de quelques classe de morphismes. III: Étude cohomologique des faisceaux cohérents (première partie)
cites work: Semisimple group schemes over complete curves
cites work: Minkowskische Reduktionstheorie über Funktionenkörpern
cites work: Chevalley groups over function fields and automorphic forms
cites work: Die Kohomologie S-arithmetischer Gruppen über Funktionenkörpern
cites work: Q4143433
cites work: Q4267924
cites work: Q4089001
cites work: Q4440466
cites work: Q4333038
cites work: Q4530238
cites work: Q3638943
cites work: Q4002684
cites work: Q2776773
cites work: Faisceaux algébriques cohérents
cites work: Q4039754
cites work: Linear algebraic groups.
cites work: Homological properties of certain arithmetic groups in the function field case
cites work: Q5557826
cites work: Q4210019
cites work: Q3884236
cites work: Adèles and algebraic groups. (Appendix 1: The case of the group \(G_2\), by M. Demazure. Appendix 2: A short survey of subsequent research on Tamagawa numbers, by T. Ono)
cites work: Basic number theory.
cites work: The Structure of Affine Buildings. (AM-168)
cites work: Finiteness Properties of Chevalley Groups over the Ring of (Laurent) Polynomials over a Finite Field
cites work: Exponential higher dimensional isoperimetric inequalities for some arithmetic groups.
cites work: Q3849050
reviewed by: L. N. Vaserstein
description: scientific article; zbMATH DE number 6087792