Linear algebraic groups
著者
書誌事項
Linear algebraic groups
（Modern Birkhäuser classics）
Birkhäuser, c2009
2nd ed
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注記
"Reprint of the 1998 second edition"
"Originally published as Volume 9 in the series Progress in Mathematics"--T.p. verso
Includes bibliographical references (p. [323]-329) and index
内容説明・目次
内容説明
The first edition of this book presented the theory of linear algebraic groups over an algebraically closed field. The second edition, thoroughly revised and expanded, extends the theory over arbitrary fields, which are not necessarily algebraically closed. It thus represents a higher aim. As in the first edition, the book includes a self-contained treatment of the prerequisites from algebraic geometry and commutative algebra, as well as basic results on reductive groups. As a result, the first part of the book can well serve as a text for an introductory graduate course on linear algebraic groups.
目次
Some Algebraic Geometry.- Linear Algebraic Groups, First Properties.- Commutative Algebraic Groups.- Derivations, Differentials, Lie Algebras.- Topological Properties of Morphisms, Applications.- Parabolic Subgroups, Borel Subgroups, Solvable Groups.- Weyl Group, Roots, Root Datum.- Reductive Groups.- The Isomorphism Theorem.- The Existence Theorem.- More Algebraic Geometry.- F-groups: General Results.- F-tori.- Solvable F-groups.- Freductive Groups.- Reductive F-Groups.- Classification.
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