000			01821nam a2200253 4500
005			20250620094623.0
008			250611b |||||||| |||| 00| 0 eng d
020			_a9781009018586
040			_aCSL _cCSL
041			_2eng _aeng
084			_aB27 Q7 NBHM _qCSL
100			_aMilne, J. S. _eauthor. _9467210
245			_aAlgebraic groups: _bThe theory of group schemes of finite type over a field
260			_aCambridge : _bCambridge Uniiversity Press, _c2017.
300			_axvi, 648 p. ; _c23 cm.
490			_aCambridge studies in advanced mathematics ; _v170
500			_aIncludes bibliography and index.
520			_aAlgebraic 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.
650			_2Affine Algebraic Groups
650			_2Isomorphism Theorems
650			_2 Tannaka Duality; Jordan Decompositions
650			_2Cohomology
942			_2CC _n0 _cTEXL _hB27 Q7 NBHM
999			_c1431614 _d1431614