Arithmetic Groups
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Introduction to Arithmetic Groups
Author | : Armand Borel |
Publsiher | : American Mathematical Soc. |
Total Pages | : 118 |
Release | : 2019-11-07 |
Genre | : Education |
ISBN | : 9781470452315 |
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Fifty years after it made the transition from mimeographed lecture notes to a published book, Armand Borel's Introduction aux groupes arithmétiques continues to be very important for the theory of arithmetic groups. In particular, Chapter III of the book remains the standard reference for fundamental results on reduction theory, which is crucial in the study of discrete subgroups of Lie groups and the corresponding homogeneous spaces. The review of the original French version in Mathematical Reviews observes that “the style is concise and the proofs (in later sections) are often demanding of the reader.” To make the translation more approachable, numerous footnotes provide helpful comments.
Arithmetic Groups
Author | : J. E. Humphreys |
Publsiher | : Springer |
Total Pages | : 166 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 9783540391982 |
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Reduction Theory and Arithmetic Groups
Author | : Joachim Schwermer |
Publsiher | : Cambridge University Press |
Total Pages | : 375 |
Release | : 2022-12-31 |
Genre | : Mathematics |
ISBN | : 9781108832038 |
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Build a solid foundation in the area of arithmetic groups and explore its inherent geometric and number-theoretical components.
Cohomology of Arithmetic Groups and Automorphic Forms
Author | : Jean-Pierre Labesse,Joachim Schwermer |
Publsiher | : Springer |
Total Pages | : 358 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 9783540468769 |
Download Cohomology of Arithmetic Groups and Automorphic Forms Book in PDF, Epub and Kindle
Cohomology of arithmetic groups serves as a tool in studying possible relations between the theory of automorphic forms and the arithmetic of algebraic varieties resp. the geometry of locally symmetric spaces. These proceedings will serve as a guide to this still rapidly developing area of mathematics. Besides two survey articles, the contributions are original research papers.
Finiteness Properties of Arithmetic Groups Acting on Twin Buildings
Author | : Stefan Witzel |
Publsiher | : Springer |
Total Pages | : 128 |
Release | : 2014-07-16 |
Genre | : Mathematics |
ISBN | : 9783319064772 |
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Providing an accessible approach to a special case of the Rank Theorem, the present text considers the exact finiteness properties of S-arithmetic subgroups of split reductive groups in positive characteristic when S contains only two places. While the proof of the general Rank Theorem uses an involved reduction theory due to Harder, by imposing the restrictions that the group is split and that S has only two places, one can instead make use of the theory of twin buildings.
Cohomology of Arithmetic Groups
Author | : James W. Cogdell,Günter Harder,Stephen Kudla,Freydoon Shahidi |
Publsiher | : Springer |
Total Pages | : 304 |
Release | : 2018-08-18 |
Genre | : Mathematics |
ISBN | : 9783319955490 |
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This book discusses the mathematical interests of Joachim Schwermer, who throughout his career has focused on the cohomology of arithmetic groups, automorphic forms and the geometry of arithmetic manifolds. To mark his 66th birthday, the editors brought together mathematical experts to offer an overview of the current state of research in these and related areas. The result is this book, with contributions ranging from topology to arithmetic. It probes the relation between cohomology of arithmetic groups and automorphic forms and their L-functions, and spans the range from classical Bianchi groups to the theory of Shimura varieties. It is a valuable reference for both experts in the fields and for graduate students and postdocs wanting to discover where the current frontiers lie.
Arithmetic Groups
Author | : James E. Humphreys |
Publsiher | : Unknown |
Total Pages | : 178 |
Release | : 1980 |
Genre | : Arithmetic groups |
ISBN | : UOM:39015046547769 |
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Twin Buildings and Applications to S Arithmetic Groups
Author | : Peter Abramenko |
Publsiher | : Springer |
Total Pages | : 131 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 9783540495703 |
Download Twin Buildings and Applications to S Arithmetic Groups Book in PDF, Epub and Kindle
This book is addressed to mathematicians and advanced students interested in buildings, groups and their interplay. Its first part introduces - presupposing good knowledge of ordinary buildings - the theory of twin buildings, discusses its group-theoretic background (twin BN-pairs), investigates geometric aspects of twin buildings and applies them to determine finiteness properties of certain S-arithmetic groups. This application depends on topological properties of some subcomplexes of spherical buildings. The background of this problem, some examples and the complete solution for all "sufficiently large" classical buildings are covered in detail in the second part of the book.