Reduction theory and arithmetic groups / Joachim Schwermer.

Format:

Book

Author/Creator:

Schwermer, Joachim, author.

Series:

New mathematical monographs ; 45.

New mathematical monographs ; 45

Language:

English

Subjects (All):

Arithmetic groups.

Number theory.

Physical Description:

1 online resource (xiii, 360 pages) : digital, PDF file(s).

Edition:

First edition.

Place of Publication:

Cambridge ; New York, NY : Cambridge University Press, 2023.

Summary:

Arithmetic groups are generalisations, to the setting of algebraic groups over a global field, of the subgroups of finite index in the general linear group with entries in the ring of integers of an algebraic number field. They are rich, diverse structures and they arise in many areas of study. This text enables you to build a solid, rigorous foundation in the subject. It first develops essential geometric and number theoretical components to the investigations of arithmetic groups, and then examines a number of different themes, including reduction theory, (semi)-stable lattices, arithmetic groups in forms of the special linear group, unipotent groups and tori, and reduction theory for adelic coset spaces. Also included is a thorough treatment of the construction of geometric cycles in arithmetically defined locally symmetric spaces, and some associated cohomological questions. Written by a renowned expert, this book is a valuable reference for researchers and graduate students.

Contents:

Modules, lattices, and orders

The general linear group over rings

A menagerie of examples - a historical perspective

Arithmetic groups

Arithmetically defined Kleinian groups and hyperbolic 3-space

Lattices - reduction theory for GL

Reduction theory and (semi)-stable lattices

Arithmetic groups in algebraic k-groups

Arithmetic groups, ambient lie groups, and related geometric objects

Geometric cycles

Geometric cycles via rational automorphisms

Reduction theory for adelic coset spaces.

Notes:

Title from publisher's bibliographic system (viewed on 05 Dec 2022).

Includes bibliographical references and index.

ISBN:

9781108935074

1108935079

9781108937610

1108937616