TY  - BOOK
AU  - Milne, J. S.
TI  - Algebraic groups: : The theory of group schemes of finite type over a field
T2  - Cambridge studies in advanced mathematics
SN  - 9781009018586
PY  - 2017///
CY  - Cambridge
PB  - Cambridge Uniiversity Press
KW  - Affine Algebraic Groups
KW  - Isomorphism Theorems
KW  -  Tannaka Duality; Jordan Decompositions
KW  - Cohomology
N1  - Includes bibliography and index
N2  - 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
ER  -