Filling a gap in the literature, this text gives a solid, rigorous foundation in the subject of the arithmetic of algebraic groups and reduction theory. It follows different developments in this area, geometric as well as number theoretical, at a level suitable for graduate students and researchers in related fields.
Filling a gap in the literature, this text gives a solid, rigorous foundation in the subject of the arithmetic of algebraic groups and reduction theory. It follows different developments in this area, geometric as well as number theoretical, at a level suitable for graduate students and researchers in related fields.
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.
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.
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