Vladimir Platonov, Andrei Rapinchuk, Igor Rapinchuk

Algebraic Groups and Number Theory: Volume 1 (eBook, PDF)

• Format: PDF

Produktbeschreibung

The first edition of this book provided the first systematic exposition of the arithmetic theory of algebraic groups. This revised second edition, now published in two volumes, retains the same goals, while incorporating corrections and improvements, as well as new material covering more recent developments. Volume I begins with chapters covering background material on number theory, algebraic groups, and cohomology (both abelian and non-abelian), and then turns to algebraic groups over locally compact fields. The remaining two chapters provide a detailed treatment of arithmetic subgroups and reduction theory in both the real and adelic settings. Volume I includes new material on groups with bounded generation and abstract arithmetic groups. With minimal prerequisites and complete proofs given whenever possible, this book is suitable for self-study for graduate students wishing to learn the subject as well as a reference for researchers in number theory, algebraic geometry, and related areas.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 31. August 2023
• Englisch
• ISBN-13: 9781009380652
• Artikelnr.: 68995234

Autorenporträt

Vladimir Platonov is Principal Research Fellow at the Steklov Mathematical Institute and the Scientific Research Institute for System Analysis of the Russian Academy of Sciences. He has made fundamental contributions to the theory of algebraic groups, including the resolution of the Kneser-Tits problem, a criterion for strong approximation in algebraic groups, and the analysis of the rationality of group varieties. His recent work brought about major progress on the problem of periodicity of continued fractions in hyperelliptic fields and investigation of torsion in the Jacobian varieties of hyperelliptic curves. A recipient of the Lenin Prize (1978) and the Chebyshev Gold Medal for outstanding results in mathematics (2022), he is currently an academician of the Russian Academy of Sciences and of the National Academy of Sciences of Belarus, and a member of the Indian National Academy of Sciences.

Inhaltsangabe

1. Algebraic number theory
2. Algebraic groups
3. Algebraic groups over locally compact fields
4. Arithmetic groups and reduction theory
5. Adeles
Bibliography
Index.