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Title: Algebraic groups : the theory of group schemes of finite type over a field (M) / J. S. Milne Dewey Class: 516.35 Author: Milne, James S., 1942- Publication: Cambridge, U.K. : Cambridge University Press, 2017 Physical Details: xvi, 644 pages : 5 b/w illus. 95 exercises; 23 cm Series: Cambridge studies in advanced mathematics; 170 ISBN: 9781107167483 Note: Online publication date:October 2017 System details note: Online access to the digital version of this printed book is available only to subscription institutions through IP address (only for SISSA internal users) Summary Note: Introduction; 1. Definitions and basic properties; 2. Examples and basic constructions; 3. Affine algebraic groups and Hopf algebras; 4. Linear representations of algebraic groups; 5. Group theory: the isomorphism theorems; 6. Subnormal series: solvable and nilpotent algebraic groups; 7. Algebraic groups acting on schemes; 8. The structure of general algebraic groups; 9. Tannaka duality: Jordan decompositions; 10. The Lie algebra of an algebraic group; 11. Finite group schemes; 12. Groups of multiplicative type: linearly reductive groups; 13. Tori acting on schemes; 14. Unipotent algebraic groups; 15. Cohomology and extensions; 16. The structure of solvable algebraic groups; 17. Borel subgroups and applications; 18. The geometry of algebraic groups; 19. Semisimple and reductive groups; 20. Algebraic groups of semisimple rank one; 21. Split reductive groups; 22. Representations of reductive groups; 23. The isogeny and existence theorems; 24. Construction of the semisimple groups; 25. Additional topics; Appendix A. Review of algebraic geometry; Appendix B. Existence of quotients of algebraic groups; Appendix C. Root data; Bibliography; Index.: ------------------------------ 0000000043902 Available at SISSA General 512.7 MIL -----------------------------------------------
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