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Reduction Theory and Arithmetic Groups

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Build a solid foundation in the area of arithmetic groups and explore its inherent geometric and number-theoretical components.

Author(s): Joachim Schwermer
Series: New Mathematical Monographs 45
Publisher: Cambridge University Press
Year: 2022

Language: English
Pages: xiv+360

Contents
Preface
Part I - Arithmetic Groups in the General Linear Group
1 - Modules, Lattices, and Orders
2 - The General Linear Group over Rings
3 - A Menagerie of Examples: A Historical Perspective
4 - Arithmetic Groups
5 - Arithmetically Defined Kleinian Groups and Hyperbolic 3-Space
Part II - Arithmetic Groups Over Global Fields
6 - Lattices: Reduction Theory for GLn
7 - Reduction Theory and (Semi)-Stable Lattices
8 - Arithmetic Groups in Algebraic k-Groups
9 - Arithmetic Groups, Ambient Lie Groups, and Related Geometric Objects
10 - Geometric Cycles
11 - Geometric Cycles via Rational Automorphisms
12 - Reduction Theory for Adelic Coset Spaces
Part III - Appendices
Appendix A Linear Algebraic Groups: A Review
Appendix B Global Fields
Appendix C Topological Groups, Homogeneous Spaces, and Proper Actions
References
Index