The Resource Algebraic groups: : the theory of group schemes of finite type over a field, J.S. Milne, University of Michigan, Ann Arbor

Algebraic groups: : the theory of group schemes of finite type over a field, J.S. Milne, University of Michigan, Ann Arbor

Label
Algebraic groups: : the theory of group schemes of finite type over a field
Title
Algebraic groups:
Title remainder
the theory of group schemes of finite type over a field
Statement of responsibility
J.S. Milne, University of Michigan, Ann Arbor
Creator
Author
Subject
Language
eng
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." -- publisher
Member of
Cataloging source
BTCTA
http://library.link/vocab/creatorDate
1942-
http://library.link/vocab/creatorName
Milne, J. S.
Dewey number
516.35
Illustrations
illustrations
Index
index present
LC call number
QA 564 .M525 2017
Literary form
non fiction
Nature of contents
bibliography
Series statement
Cambridge studies in advanced mathematics
Series volume
170
http://library.link/vocab/subjectName
  • Geometry, Algebraic
  • Group theory
Label
Algebraic groups: : the theory of group schemes of finite type over a field, J.S. Milne, University of Michigan, Ann Arbor
Instantiates
Publication
Note
Includes references (p.627-636) and index
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Definitions and basic properties -- Examples and basic constructions -- Affine algebraic groups and Hopf algebras -- Linear representations of algebraic groups -- Group theory: the isomorphism theorems -- Subnormal series; solvable and nilpotent algebraic groups -- Algebraic groups acting on schemes -- The structure of general algebraic groups -- The structure of general algebraic groups -- Tannaka duality; Jordan decompositions -- The Lie algebra of an algebraic group -- Finite group schemes -- Groups of multiplicative type; linearly reductive groups -- Tori acting on schemes -- Unipotent algebraic groups -- Cohomology and extensions -- The structure of solvable algebraic groups -- Borel subgroups and applications -- The geometry of algebraic groups -- Semisimple and reductive groups -- Algebraic groups of semisimple rank one -- Split reductive groups -- Representations of reductive groups -- The isogeny and existence theorems -- Construction of the semisimple groups -- Additional topics -- Appendix A: Review of algebraic geometry -- Appendix B: Existence of quotients of algebraic groups -- Appendix C: Root data
Dimensions
24cm.
Extent
xiv, 644 pages:
Isbn
9781107167483
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
Other physical details
illustrations;
System control number
  • (OCoLC)992433996
  • (OCoLC)ocn992433996
Label
Algebraic groups: : the theory of group schemes of finite type over a field, J.S. Milne, University of Michigan, Ann Arbor
Publication
Note
Includes references (p.627-636) and index
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Definitions and basic properties -- Examples and basic constructions -- Affine algebraic groups and Hopf algebras -- Linear representations of algebraic groups -- Group theory: the isomorphism theorems -- Subnormal series; solvable and nilpotent algebraic groups -- Algebraic groups acting on schemes -- The structure of general algebraic groups -- The structure of general algebraic groups -- Tannaka duality; Jordan decompositions -- The Lie algebra of an algebraic group -- Finite group schemes -- Groups of multiplicative type; linearly reductive groups -- Tori acting on schemes -- Unipotent algebraic groups -- Cohomology and extensions -- The structure of solvable algebraic groups -- Borel subgroups and applications -- The geometry of algebraic groups -- Semisimple and reductive groups -- Algebraic groups of semisimple rank one -- Split reductive groups -- Representations of reductive groups -- The isogeny and existence theorems -- Construction of the semisimple groups -- Additional topics -- Appendix A: Review of algebraic geometry -- Appendix B: Existence of quotients of algebraic groups -- Appendix C: Root data
Dimensions
24cm.
Extent
xiv, 644 pages:
Isbn
9781107167483
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
Other physical details
illustrations;
System control number
  • (OCoLC)992433996
  • (OCoLC)ocn992433996

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