Joachim Schwermer

Reduction Theory and Arithmetic Groups (eBook, PDF)

• Format: PDF

Produktbeschreibung

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

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 15. Dezember 2022
• Englisch
• ISBN-13: 9781108935074
• Artikelnr.: 70911494

Autorenporträt

Joachim Schwermer is Emeritus Professor of Mathematics at the University of Vienna, and recently Guest Researcher at the Max-Planck-Institute for Mathematics, Bonn. He was Director of the Erwin-Schrödinger-Institute for Mathematics and Physics, Vienna from 2011 to 2016. His research focuses on questions arising in the arithmetic of algebraic groups and the theory of automorphic forms.

Inhaltsangabe

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
Appendices: A. Linear algebraic groups - a review
B. Global fields
C. Topological groups, homogeneous spaces, and proper actions
References
Index.