---

＜電子ブック＞
Serre's Problem on Projective Modules / by T.Y. Lam
(Springer Monographs in Mathematics. ISSN:21969922)

版	1st ed. 2006.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2006
本文言語	英語
大きさ	XXII, 404 p : online resource
著者標目	*Lam, T.Y author SpringerLink (Online service)
件　名	LCSH:Commutative algebra LCSH:Commutative rings LCSH:Associative rings LCSH:Associative algebras FREE:Commutative Rings and Algebras FREE:Associative Rings and Algebras
一般注記	to 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 “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 HTTP:URL=https://doi.org/10.1007/978-3-540-34575-6

 類似資料