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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
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The item Algebraic groups : the theory of group schemes of finite type over a field, J.S. Milne, University of Michigan, Ann Arbor represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.This item is available to borrow from all library branches.
Resource Information
The item Algebraic groups : the theory of group schemes of finite type over a field, J.S. Milne, University of Michigan, Ann Arbor represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.
This item is available to borrow from all library branches.
 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."  publisher
 Language
 eng
 Extent
 xvi, 644 pages:
 Note
 Includes references (pages 627636) and index
 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
 Isbn
 9781107167483
 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
 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 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."  publisher
 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
 QA564
 LC item number
 .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
 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
 Note
 Includes references (pages 627636) 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
 xvi, 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
 Note
 Includes references (pages 627636) 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
 xvi, 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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