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The Resource Serre's problem on projective modules, Tsit-Yuen Lam

Serre's problem on projective modules, Tsit-Yuen Lam

Label
Serre's problem on projective modules
Title
Serre's problem on projective modules
Statement of responsibility
Tsit-Yuen Lam
Creator
Author
Subject
Language
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 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
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorDate
1942-
http://library.link/vocab/creatorName
Lam, T. Y.
Dewey number
516.3/5
Index
index present
LC call number
QA247.3
LC item number
.L35 2006
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Springer Monographs in Mathematics,
http://library.link/vocab/subjectName
  • Projective modules (Algebra)
  • Commutative algebra
  • Geometry, Algebraic
  • Modules projectifs (Algèbre)
  • Algèbre commutative
  • Géométrie algébrique
  • Commutative algebra
  • Geometry, Algebraic
  • Projective modules (Algebra)
  • Serre-Vermutung
  • Anéis e álgebras comutativos
Label
Serre's problem on projective modules, Tsit-Yuen Lam
Instantiates
Publication
Note
Revised edition of author's "Serre's conjecture," 1978
Bibliography note
Includes bibliographical references (pages 271-276 and pages 363-393) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • New developments (since 1977)
  • Introduction to Serre's conjecture: 1955-1976
  • Foundations
  • The "classical" results on Serre's conjecture
  • The basic calculus of unimodular rows
  • Horrock's theorem
  • Quillen's methods
  • K1-analogue of Serre's conjecture
  • The quadratic analogue of Serre's conjecture
Control code
655778570
Dimensions
unknown
Extent
1 online resource (xxi, 401 pages).
Form of item
online
Isbn
9783540345756
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-540-34575-6
http://library.link/vocab/ext/overdrive/overdriveId
978-3-540-23317-6
Publisher number
10891306
Specific material designation
remote
System control number
(OCoLC)655778570
Label
Serre's problem on projective modules, Tsit-Yuen Lam
Publication
Note
Revised edition of author's "Serre's conjecture," 1978
Bibliography note
Includes bibliographical references (pages 271-276 and pages 363-393) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • New developments (since 1977)
  • Introduction to Serre's conjecture: 1955-1976
  • Foundations
  • The "classical" results on Serre's conjecture
  • The basic calculus of unimodular rows
  • Horrock's theorem
  • Quillen's methods
  • K1-analogue of Serre's conjecture
  • The quadratic analogue of Serre's conjecture
Control code
655778570
Dimensions
unknown
Extent
1 online resource (xxi, 401 pages).
Form of item
online
Isbn
9783540345756
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-540-34575-6
http://library.link/vocab/ext/overdrive/overdriveId
978-3-540-23317-6
Publisher number
10891306
Specific material designation
remote
System control number
(OCoLC)655778570

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