000			03233nam a22003978i 4500
001			CR9781316092439
003			UkCbUP
005			20200124160212.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			140508s2015||||enk o ||1 0|eng|d
020			_a9781316092439 (ebook)
020			_z9781107087231 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA179 _b.C667 2015
082	0	0	_a512/.55 _222
100	1		_aConrad, Brian, _d1970- _eauthor.
245	1	0	_aPseudo-reductive groups / _cBrian Conrad, Stanford University, Ofer Gabber, Institut des hautes études scientifiques, Gopal Prasad, University of Michigan.
250			_aSecond edition.
264		1	_aCambridge : _bCambridge University Press, _c2015.
300			_a1 online resource (xxiv, 665 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aNew mathematical monographs ; _v26
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_aIntroduction -- Terminology, conventions, and notation -- Part I: Constructions, Examples, and Structure Theory. 1. Overview of pseudo-reductivity ; 2. Root groups and root systems ; 3. Basic structure theory -- Part II: Standard Presentations and Their Applications. 4. Variation of (G', k'/k, T', C) ; 5. Ubiquity of the standard construction ; 6. Classification results -- Part III: General Classification and Applications. 7. The exotic constructions ; 8. Preparations for classification in characteristics 2 and 3 ; 9. Absolutely pseudo-simple groups in characteristic 2 ; 10. General case ; 11. Applications -- Part IV: Appendices. A. Background in linear algebraic groups ; B. Tits' work on unipotent groups in nonzero characteristic ; C. Rational conjugacy in connected groups -- References -- Index.
520			_aPseudo-reductive groups arise naturally in the study of general smooth linear algebraic groups over non-perfect fields and have many important applications. This monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. In this second edition there is new material on relative root systems and Tits systems for general smooth affine groups, including the extension to quasi-reductive groups of famous simplicity results of Tits in the semisimple case. Chapter 9 has been completely rewritten to describe and classify pseudo-split absolutely pseudo-simple groups with a non-reduced root system over arbitrary fields of characteristic 2 via the useful new notion of 'minimal type' for pseudo-reductive groups. Researchers and graduate students working in related areas, such as algebraic geometry, algebraic group theory, or number theory will value this book, as it develops tools likely to be used in tackling other problems.
650		0	_aLinear algebraic groups.
650		0	_aGroup theory.
700	1		_aGabber, Ofer, _d1958- _eauthor.
700	1		_aPrasad, Gopal, _eauthor.
776	0	8	_iPrint version: _z9781107087231
830		0	_aNew mathematical monographs ; _v26.
856	4	0	_uhttps://doi.org/10.1017/CBO9781316092439
999			_c515951 _d515949