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Reduction theory and arithmetic groups / Joachim Schwermer.

By: Material type: TextTextSeries: New mathematical monographs ; 45.Publisher: Cambridge ; New York, NY : Cambridge University Press, 2023Copyright date: ©2023Description: xiii, 360 pages : illustrations ; 25 cmContent type:
  • text
Media type:
  • unmediated
Carrier type:
  • volume
ISBN:
  • 9781108832038
  • 1108832032
Subject(s): DDC classification:
  • 512.74 23/eng20220902
LOC classification:
  • QA174.2 .S349 2023
  • QA174.2 .S349 2023
Contents:
Modules, lattices, and orders -- The general linear group over rings -- A menagerie of examples -- a historical perspective -- Arithmetic groups -- Arithmetically defined Kleinian groups and hyperbolic 3-space -- Lattices -- reduction theory for GL -- Reduction theory and (semi)-stable lattices -- Arithmetic groups in algebraic k-groups -- Arithmetic groups, ambient lie groups, and related geometric objects -- Geometric cycles -- Geometric cycles via rational automorphisms -- Reduction theory for adelic coset spaces.
Summary: "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"-- Provided by publisher.
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Includes bibliographical references and index.

Modules, lattices, and orders -- The general linear group over rings -- A menagerie of examples -- a historical perspective -- Arithmetic groups -- Arithmetically defined Kleinian groups and hyperbolic 3-space -- Lattices -- reduction theory for GL -- Reduction theory and (semi)-stable lattices -- Arithmetic groups in algebraic k-groups -- Arithmetic groups, ambient lie groups, and related geometric objects -- Geometric cycles -- Geometric cycles via rational automorphisms -- Reduction theory for adelic coset spaces.

"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"-- Provided by publisher.

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