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020			_a0821842455 _qPaperback
020			_a9780821842454 _qPaperback
040			_aNISER LIBRARY _beng _cNISER LIBRARY
082	0	4	_a514.7 _bFAN-F
245	1	0	_aFundamental algebraic geometry : _bGrothendieck's FGA explained
260			_aProvidence, R.I. : _bAmerican Mathematical Society, _c2005.
300			_ax, 339 pages ; _c27 cm.
490			_aMathematical surveys and monographs, _vv. 123 _x0076-5376 ;
504			_aIncludes bibliographical references (p. 323-331) and index.
520			_aAlexander Grothendieck's concepts turned out to be astoundingly powerful and productive, truly revolutionizing algebraic geometry. He sketched his new theories in talks given at the Séminaire Bourbaki between 1957 and 1962. He then collected these lectures in a series of articles in Fondements de la géométrie algébrique (commonly known as FGA). Much of FGA is now common knowledge. However, some of it is less well known, and only a few geometers are familiar with its full scope. The goal of the current book, which resulted from the 2003 Advanced School in Basic Algebraic Geometry (Trieste, Italy), is to fill in the gaps in Grothendieck's very condensed outline of his theories. The four main themes discussed in the book are descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. The authors present complete proofs of the main results, using newer ideas to promote understanding whenever necessary, and drawing connections to later developments. With the main prerequisite being a thorough acquaintance with basic scheme theory, this book is a valuable resource for anyone working in algebraic geometry.
521			_aReadership: Graduate students and research mathematicians interested in algebraic geometry.
650		0	_aGeometry, Algebraic
650		0	_aGrothendieck groups
650		0	_aGrothendieck categories
700	1		_aFantechi, Barbara
700	1		_aGöttsche, Lothar
700	1		_aIllusie, Luc
700	1		_aKleiman, Steven L.
700	1		_aNitsure, Nitin
700	1		_aVistoli, Angelo
856	4	1	_3Table of contents _uhttps://www.ams.org/books/surv/123/surv123-endmatter.pdf
856	4	1	_3Reviews _uhttps://www.goodreads.com/book/show/2170336.Fundamental_Algebraic_Geometry?ref=nav_sb_ss_1_13#CommunityReviews
942			_cBK _2udc
999			_c36284 _d36284