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Algebraic Groups and Number Theory: Volume 1 (Hardcover, 2nd Revised edition)
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Algebraic Groups and Number Theory: Volume 1 (Hardcover, 2nd Revised edition)
Series: Cambridge Studies in Advanced Mathematics
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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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