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Algebraic Groups

The Theory Of Group Schemes Of Finite Type Over A Field

Algebraic Groups - Milne, J. S. (university Of Michigan, Ann Arbor) - ISBN: 9781107167483
Prijs: € 106,85
Levertijd: 8 tot 12 werkdagen
Bindwijze: Boek, Gebonden
Genre: Wiskunde algemeen
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Beschrijving

Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.

Details

Titel: Algebraic Groups
auteur: Milne, J. S. (university Of Michigan, Ann Arbor)
Mediatype: Boek
Bindwijze: Gebonden
Taal: Engels
Aantal pagina's: 660
Uitgever: Cambridge University Press
Plaats van publicatie: 03
NUR: Wiskunde algemeen
Afmetingen: 228 x 152 x 41
Gewicht: 1050 gr
ISBN/ISBN13: 9781107167483
Intern nummer: 39111771

Biografie (woord)

J. S. Milne is Professor Emeritus at the University of Michigan, Ann Arbor. His previous books include Etale Cohomology (1980) and Arithmetic Duality Theorems (2006).

Quote

'All together, this excellent text fills a long-standing gap in the textbook literature on algebraic groups. It presents the modern theory of group schemes in a very comprehensive, systematic, detailed and lucid manner, with numerous illustrating examples and exercises. It is fair to say that this reader-friendly textbook on algebraic groups is the long-desired modern successor to the old, venerable standard primers mentioned above.' Werner Kleinert, zbMath

Inhoudsopgave

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.

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