Algebraic groups : the theory of group schemes of finite type over a field
 Responsibility
 J.S. Milne, University of Michigan, Ann Arbor.
 Publication
 Cambridge, United Kingdom ; New York, New York : Cambridge University Press, [2017]
 Copyright notice
 ©2017
 Physical description
 xiv, 644 pages : illustrations ; 24cm.
 Series
 Cambridge studies in advanced mathematics ; 170.
At the library
Science Library (Li and Ma)
Stacks
Call number  Status 

QA564 .M525 2017  Unknown 
More options
Description
Creators/Contributors
 Author/Creator
 Milne, J. S., 1942 author.
Contents/Summary
 Contents

 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.
 (source: Nielsen Book Data)
 Publisher's Summary
 ["Algebraic groups play much the same role for algebraists as Lie groups play for analysts. This book is the first comprehensive introduction to the theory of algebraic group schemes over fields that includes the structure theory of semisimple algebraic groups, and is written in the language of modern algebraic geometry. The first eight chapters study general algebraic group schemes over a field and culminate in a proof of the BarsottiChevalley theorem, realizing every algebraic group as an extension of an abelian variety by an affine group. After a review of the Tannakian philosophy, the author provides short accounts of Lie algebras and finite group schemes. The later chapters treat reductive algebraic groups over arbitrary fields, including the BorelChevalley structure theory. Solvable algebraic groups are studied in detail. Prerequisites have also been kept to a minimum so that the book is accessible to nonspecialists in algebraic geometry.", {"source"=>"(source: Nielsen Book Data)"}, "9781107167483", "20171009"]
Subjects
Bibliographic information
 Publication date
 2017
 Series
 Cambridge studies in advanced mathematics ; 170
 Note
 Includes references (p.627636) and index.
 ISBN
 9781107167483
 1107167485