Algebraic Groups and Number Theory

Platonov, Vladimir; Rapinchuk, Andrei; Rapinchuk, Igor

ISBN 10: 052111361X / ISBN 13: 9780521113618

Published by Cambridge Univ Pr, 2023

About this Item

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Bibliographic Details

• Title: Algebraic Groups and Number Theory
• Publisher: Cambridge Univ Pr
• Publication Date: 2023
• Language: English
• ISBN 10: 052111361X
• ISBN 13: 9780521113618
• Binding: Hardcover
• Edition: 2nd Edition
• Condition: As New

About this title

Synopsis

The first volume of a two-volume book offering a comprehensive account of the arithmetic theory of algebraic groups.

About the Authors

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.

Andrei Rapinchuk is McConnell-Bernard Professor of Mathematics at the University of Virginia. His contributions to the arithmetic theory of algebraic groups include a variety of results concerning the normal subgroup structure of the groups of rational points of algebraic groups, the congruence subgroup and metaplectic problems, and different aspects of the local-global principle. He has also applied the theory of arithmetic groups to investigate isospectral locally symmetric spaces.

Igor Rapinchuk is Associate Professor of Mathematics at Michigan State University. His current research deals mainly with the emerging arithmetic theory of algebraic groups over higher-dimensional fields, focusing on finiteness properties of groups with good reduction, local-global principles, and abstract homomorphisms.