ENGLISH

Algebraic groups. The theory of group schemes of finite type over a field

By Milne J.S.

Book information

Publisher
Cambridge University Press
Year
2017
ISBN
978-1-107-16748-3, 1107167485, 9781316711736
Language
english
Format
PDF
Filesize
3 MB (2936462 bytes)
Pages
660\660
Topic
Mathematics Algebra
Library
kolxo3
Time added
2019-04-25 18:00:00

Description

Content: 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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