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  1. Home
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  3. Reduction Theory and Arithmetic Groups
  • Cited by 1
Publisher:
Cambridge University Press
Online publication date:
December 2022
Print publication year:
2022
Online ISBN:
9781108937610
DOI:
https://doi.org/10.1017/9781108937610
Subjects:
Mathematics (general), Mathematics, Number Theory, Algebra
Series:
New Mathematical Monographs (45)
Information

Book description

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.

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