Online Public Access Catalogue (OPAC)
Library,Documentation and Information Science Division

“A research journal serves that narrow

borderland which separates the known from the unknown”

-P.C.Mahalanobis


Normal view MARC view ISBD view

Algebraic groups: the theory of group schemes of finite type over a field/ J S Milne

By: Milne, J S [author].
Series: Cambridge Studies in Advanced Mathematics. Cambridge Studies in Advanced Mathematics 170.Publisher: UK: CUP, 2017Description: xvi, 644 pages 23cm.ISBN: 978-1107167483.Subject(s): Mathematics | Algebraic Groups | Lie Group | Finite Group | Algebraic GeometryDDC classification: 516.35 Online resources: Click here to access online
Contents:
Preface, Introduction, Conventions and notation, 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 theorem, 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, Finite group schemes, 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 Roof data, References, Index
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 Barsotti–Chevalley 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 Borel–Chevalley structure theory. Solvable algebraic groups are studied in detail. Prerequisites have also been kept to a minimum so that the book is accessible to non-specialists in algebraic geometry.
Tags from this library: No tags from this library for this title. Log in to add tags.
Item type Current location Call number Status Date due Barcode Item holds
Books Books ISI Library, Kolkata
 
516.35 M659 (Browse shelf) Available 138447
Total holds: 0

Includes bibliographical reference and index

Preface,
Introduction,
Conventions and notation,
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 theorem,
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, Finite group schemes,
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 Roof data,
References,
Index

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 Barsotti–Chevalley 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 Borel–Chevalley structure theory. Solvable algebraic groups are studied in detail. Prerequisites have also been kept to a minimum so that the book is accessible to non-specialists in algebraic geometry.

There are no comments for this item.

Log in to your account to post a comment.
Library, Documentation and Information Science Division, Indian Statistical Institute, 203 B T Road, Kolkata 700108, INDIA
Phone no. 91-33-2575 2100, Fax no. 91-33-2578 1412, ksatpathy@isical.ac.in


Visitor Counter