Joachim Schwermer

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.

Reduction Theory and Arithmetic Groups

Jean-Pierre Labesse

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.

Proceedings of a Conference held in Luminy/Marseille, France, May 22-27, 1989

Cohomology of Arithmetic Groups and Automorphic Forms

Friedrich Hirzebruch

Silke Suter

Proceedings of the Meeting held by the Max-Planck-Institut für Mathematik, Bonn, June 15-22, 1984

Arbeitstagung Bonn 1984

Catherine Goldstein

Norbert Schappacher

Since its publication, C.F. Gauss's Disquisitiones Arithmeticae (1801) has acquired an almost mythical reputation, standing as an ideal of exposition in notation, problems and methods; as a model of organisation and theory building; and as a source of mathematical inspiration. Eighteen authors - mathematicians, historians, philosophers - have collaborated in this volume to assess the impact of the Disquisitiones, in the two centuries since its publication.

The Shaping of Arithmetic after C.F. Gauss's Disquisitiones Arithmeticae

Joachim Schwermer

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