000			02207nam a22003498i 4500
001			CR9781316711736
003			UkCbUP
005			20200124160208.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			160204s2017||||enk o ||1 0|eng|d
020			_a9781316711736 (ebook)
020			_z9781107167483 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050		4	_aQA179 _b.M55 2017
082	0	4	_a516/.35 _223
100	1		_aMilne, J. S., _d1942- _eauthor.
245	1	0	_aAlgebraic groups : _bthe theory of group schemes of finite type over a field / _cJ. S. Milne.
264		1	_aCambridge : _bCambridge University Press, _c2017.
300			_a1 online resource (xvi, 644 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aCambridge studies in advanced mathematics ; _v170
500			_aTitle from publisher's bibliographic system (viewed on 24 Oct 2017).
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		0	_aLinear algebraic groups.
650		0	_aGroup theory.
776	0	8	_iPrint version: _z9781107167483
830		0	_aCambridge studies in advanced mathematics ; _v170.
856	4	0	_uhttps://doi.org/10.1017/9781316711736
999			_c515568 _d515566