000			03477nam a22004815i 4500
001			978-3-540-34575-6
003			DE-He213
005			20161121231034.0
007			cr nn 008mamaa
008			100514s2006 gw | s |||| 0|eng d
020			_a9783540345756 _9978-3-540-34575-6
024	7		_a10.1007/978-3-540-34575-6 _2doi
050		4	_aQA251.3
072		7	_aPBF _2bicssc
072		7	_aMAT002010 _2bisacsh
082	0	4	_a512.44 _223
100	1		_aLam, Tsit Yuen. _eauthor.
245	1	0	_aSerre’s Problem on Projective Modules _h[electronic resource] / _cby Tsit Yuen Lam.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2006.
300			_aXXII, 404 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aSpringer Monographs in Mathematics, _x1439-7382
505	0		_ato Serre’s Conjecture: 1955–1976 -- Foundations -- The “Classical” Results on Serre’s Conjecture -- The Basic Calculus of Unimodular Rows -- Horrocks’ Theorem -- Quillen’s Methods -- K1-Analogue of Serre’s Conjecture -- The Quadratic Analogue of Serre’s Conjecture -- References for Chapters I–VII -- Appendix: Complete Intersections and Serre’s Conjecture -- New Developments (since 1977) -- References for Chapter VIII.
520			_a“Serre’s Conjecture”, for the most part of the second half of the 20th century, - ferred to the famous statement made by J. -P. Serre in 1955, to the effect that one did not know if ?nitely generated projective modules were free over a polynomial ring k[x ,. . . ,x], where k is a ?eld. This statement was motivated by the fact that 1 n the af?ne scheme de?ned by k[x ,. . . ,x] is the algebro-geometric analogue of 1 n the af?ne n-space over k. In topology, the n-space is contractible, so there are only trivial bundles over it. Would the analogue of the latter also hold for the n-space in algebraic geometry? Since algebraic vector bundles over Speck[x ,. . . ,x] corre- 1 n spond to ?nitely generated projective modules over k[x ,. . . ,x], the question was 1 n tantamount to whether such projective modules were free, for any base ?eld k. ItwasquiteclearthatSerreintendedhisstatementasanopenproblemintheshe- theoretic framework of algebraic geometry, which was just beginning to emerge in the mid-1950s. Nowhere in his published writings had Serre speculated, one way or another, upon the possible outcome of his problem. However, almost from the start, a surmised positive answer to Serre’s problem became known to the world as “Serre’s Conjecture”. Somewhat later, interest in this “Conjecture” was further heightened by the advent of two new (and closely related) subjects in mathematics: homological algebra, and algebraic K-theory.
650		0	_aMathematics.
650		0	_aAssociative rings.
650		0	_aRings (Algebra).
650		0	_aCommutative algebra.
650		0	_aCommutative rings.
650	1	4	_aMathematics.
650	2	4	_aCommutative Rings and Algebras.
650	2	4	_aAssociative Rings and Algebras.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783540233176
830		0	_aSpringer Monographs in Mathematics, _x1439-7382
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-540-34575-6
912			_aZDB-2-SMA
950			_aMathematics and Statistics (Springer-11649)
999			_c507638 _d507638