An adelic arithmeticity theorem for lattices in products

Uri Bader; Alex Furman; Roman Sauer

doi:10.1007/s00209-019-02241-9

An adelic arithmeticity theorem for lattices in products

Uri Bader
, Alex Furman
, Roman Sauer

Department of Mathematics

Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we prove that, under mild assumptions, a lattice in a product of semi-simple Lie group and a totally disconnected locally compact group is, in a certain sense, arithmetic. We do not assume the lattice to be finitely generated or the ambient group to be compactly generated.

Original language	English
Pages (from-to)	1181-1199
Number of pages	19
Journal	Mathematische Zeitschrift
Volume	293
Issue number	3-4
Early online date	24 Jan 2019
DOIs	https://doi.org/10.1007/s00209-019-02241-9
State	Published - 1 Dec 2019

Keywords

Adels
Algebraic group
Arithmetic group
Lattice
tdlc group

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/s00209-019-02241-9

http://arxiv.org/abs/1705.08158License: Other

Cite this

@article{de5d65a3fabc40a28756a379e8fd299f,

title = "An adelic arithmeticity theorem for lattices in products",

abstract = "In this paper we prove that, under mild assumptions, a lattice in a product of semi-simple Lie group and a totally disconnected locally compact group is, in a certain sense, arithmetic. We do not assume the lattice to be finitely generated or the ambient group to be compactly generated.",

keywords = "Adels, Algebraic group, Arithmetic group, Lattice, tdlc group",

author = "Uri Bader and Alex Furman and Roman Sauer",

note = "Publisher Copyright: {\textcopyright} 2019, Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2019",

month = dec,

day = "1",

doi = "10.1007/s00209-019-02241-9",

language = "English",

volume = "293",

pages = "1181--1199",

journal = "Mathematische Zeitschrift",

issn = "0025-5874",

publisher = "Springer New York",

number = "3-4",

}

TY - JOUR

T1 - An adelic arithmeticity theorem for lattices in products

AU - Bader, Uri

AU - Furman, Alex

AU - Sauer, Roman

PY - 2019/12/1

Y1 - 2019/12/1

N2 - In this paper we prove that, under mild assumptions, a lattice in a product of semi-simple Lie group and a totally disconnected locally compact group is, in a certain sense, arithmetic. We do not assume the lattice to be finitely generated or the ambient group to be compactly generated.

AB - In this paper we prove that, under mild assumptions, a lattice in a product of semi-simple Lie group and a totally disconnected locally compact group is, in a certain sense, arithmetic. We do not assume the lattice to be finitely generated or the ambient group to be compactly generated.

KW - Adels

KW - Algebraic group

KW - Arithmetic group

KW - Lattice

KW - tdlc group

UR - https://www.scopus.com/pages/publications/85060688604

U2 - 10.1007/s00209-019-02241-9

DO - 10.1007/s00209-019-02241-9

M3 - Article

SN - 0025-5874

VL - 293

SP - 1181

EP - 1199

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3-4

ER -

An adelic arithmeticity theorem for lattices in products

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this