紹介
The structure and classification of reductive groups over arbitrary fields has become a standard part of mathematics, with broad connections to many aspects of group theory (Lie groups), number theory (Langlands program, arithmetic groups), algebraic geometry and invariant theory. The first ten chapters of this text cover the theory of linear algebraic groups over algebraically closed fields, culminating in the theory of reductive groups, and includes the uniqueness and existence theorems. Chapters 11-17 cover the theory of linear algebraic groups which are not algebraically closed. The last seven chapters deal with the Tits classification of simple groups. The work is concise and self-contained, and should appeal to a broad audience of graduate students and researchers in the field. It is suitable for use as a textbook for a course on the theory, and contains exercises.
目次
Some algebraic geometry
linear algebraic groups, first properties
communtative algebraic groups
derivations, differntials, 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
F-reductive groups
reductive F-groups
classification.
