The Resource Serre's problem on projective modules, TsitYuen Lam
Serre's problem on projective modules, TsitYuen Lam
Resource Information
The item Serre's problem on projective modules, TsitYuen Lam represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Serre's problem on projective modules, TsitYuen Lam represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 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
 Language
 eng
 Extent
 1 online resource (xxi, 401 pages).
 Note
 Revised edition of author's "Serre's conjecture," 1978
 Contents

 New developments (since 1977)
 Introduction to Serre's conjecture: 19551976
 Foundations
 The "classical" results on Serre's conjecture
 The basic calculus of unimodular rows
 Horrock's theorem
 Quillen's methods
 K1analogue of Serre's conjecture
 The quadratic analogue of Serre's conjecture
 Isbn
 9783540345756
 Label
 Serre's problem on projective modules
 Title
 Serre's problem on projective modules
 Statement of responsibility
 TsitYuen Lam
 Subject

 Commutative algebra
 Commutative algebra
 Commutative algebra
 Geometry, Algebraic
 Geometry, Algebraic
 Geometry, Algebraic
 Géométrie algébrique
 Modules projectifs (Algèbre)
 Projective modules (Algebra)
 Projective modules (Algebra)
 Projective modules (Algebra)
 SerreVermutung
 Algèbre commutative
 Anéis e álgebras comutativos
 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 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
 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)
 SerreVermutung
 Anéis e álgebras comutativos
 Label
 Serre's problem on projective modules, TsitYuen Lam
 Note
 Revised edition of author's "Serre's conjecture," 1978
 Bibliography note
 Includes bibliographical references (pages 271276 and pages 363393) 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: 19551976
 Foundations
 The "classical" results on Serre's conjecture
 The basic calculus of unimodular rows
 Horrock's theorem
 Quillen's methods
 K1analogue 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
 10.1007/9783540345756
 http://library.link/vocab/ext/overdrive/overdriveId
 9783540233176
 Publisher number
 10891306
 Specific material designation
 remote
 System control number
 (OCoLC)655778570
 Label
 Serre's problem on projective modules, TsitYuen Lam
 Note
 Revised edition of author's "Serre's conjecture," 1978
 Bibliography note
 Includes bibliographical references (pages 271276 and pages 363393) 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: 19551976
 Foundations
 The "classical" results on Serre's conjecture
 The basic calculus of unimodular rows
 Horrock's theorem
 Quillen's methods
 K1analogue 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
 10.1007/9783540345756
 http://library.link/vocab/ext/overdrive/overdriveId
 9783540233176
 Publisher number
 10891306
 Specific material designation
 remote
 System control number
 (OCoLC)655778570
Subject
 Commutative algebra
 Commutative algebra
 Commutative algebra
 Geometry, Algebraic
 Geometry, Algebraic
 Geometry, Algebraic
 Géométrie algébrique
 Modules projectifs (Algèbre)
 Projective modules (Algebra)
 Projective modules (Algebra)
 Projective modules (Algebra)
 SerreVermutung
 Algèbre commutative
 Anéis e álgebras comutativos
Member of
Library Links
Embed
Settings
Select options that apply then copy and paste the RDF/HTML data fragment to include in your application
Embed this data in a secure (HTTPS) page:
Layout options:
Include data citation:
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.missouri.edu/portal/SerresproblemonprojectivemodulesTsitYuen/fXTbq1A77Qs/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/SerresproblemonprojectivemodulesTsitYuen/fXTbq1A77Qs/">Serre's problem on projective modules, TsitYuen Lam</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>
Note: Adjust the width and height settings defined in the RDF/HTML code fragment to best match your requirements
Preview
Cite Data  Experimental
Data Citation of the Item Serre's problem on projective modules, TsitYuen Lam
Copy and paste the following RDF/HTML data fragment to cite this resource
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.missouri.edu/portal/SerresproblemonprojectivemodulesTsitYuen/fXTbq1A77Qs/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/SerresproblemonprojectivemodulesTsitYuen/fXTbq1A77Qs/">Serre's problem on projective modules, TsitYuen Lam</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>