Serre's Problem on Projective Modules
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The work Serre's Problem on Projective Modules represents a distinct intellectual or artistic creation found in University of Oklahoma Libraries. This resource is a combination of several types including: Work, Language Material, Books.
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Serre's Problem on Projective Modules
Resource Information
The work Serre's Problem on Projective Modules represents a distinct intellectual or artistic creation found in University of Oklahoma Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Serre's Problem on Projective Modules
 Statement of responsibility
 by T.Y. Lam
 Language

 eng
 eng
 Summary
 “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 algebrogeometric analogue of 1 n the af?ne nspace over k. In topology, the nspace is contractible, so there are only trivial bundles over it. Would the analogue of the latter also hold for the nspace 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 mid1950s. 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 Ktheory
 Dewey number
 512.4
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
 qb8LLLI5zig
 Language note
 English
 LC call number
 QA251.3
 Literary form
 non fiction
 Nature of contents
 dictionaries
 Series statement
 Springer Monographs in Mathematics,
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