| 书目名称 | Serre‘s Problem on Projective Modules | | 编辑 | Tsit Yuen Lam | | 视频video | | | 概述 | An invaluable summary of research work done in the period from 1978 to the present | | 丛书名称 | Springer Monographs in Mathematics | | 图书封面 |  | | 描述 | “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 pr | | 出版日期 | Book 2006 | | 关键词 | Area; Calc; Factor; Microsoft Access; Serre‘s Conjecture; Serre‘s problem; boundary element method; calculu | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-540-34575-6 | | isbn_softcover | 978-3-642-06235-3 | | isbn_ebook | 978-3-540-34575-6Series ISSN 1439-7382 Series E-ISSN 2196-9922 | | issn_series | 1439-7382 | | copyright | Springer-Verlag Berlin Heidelberg 2006 |
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发表于 2025-3-21 19:44:02
