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MARC 21

Algebraic groups: the theory of group schemes of finite type over a field
Tag	Description
020	$a9781107167483
082	$a516.35
099	$a512.7 MIL
100	$aMilne, James S.$d1942-
245	$aAlgebraic groups$bthe theory of group schemes of finite type over a field$hM$cJ. S. Milne
260	$aCambridge, U.K.$bCambridge University Press$c2017
300	$axvi, 644 pages$b5 b/w illus. 95 exercises$c23 cm
440	$aCambridge studies in advanced mathematics$v170
500	$aOnline publication date:October 2017
520	$aIntroduction; 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.
538	$aOnline access to the digital version of this printed book is available only to subscription institutions through IP address (only for SISSA internal users)