Serre s problem on projective modules
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...
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| Main Author: | |
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| Format: | Livre numérique |
| Language: | Anglais |
| Published: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Edition: | 1st ed. 2006. |
| Series: | Springer Monographs in Mathematics
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| Subjects: | |
| Online Access: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Note: |
Description d'après consultation du 22 avril 2011 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Variante du titre: | Serre's conjecture |
| Edition sous un autre format: | • Serre's problem on projective modules, T. Y. Lam, 2006, Berlin, Springer, 1 vol. (XXI-401 p.), Springer monographs in mathematics, 3-540-23317-2 • Serre's Problem on Projective Modules, Texte imprimé, 9783540860563 • Serre's Problem on Projective Modules, Texte imprimé, 9783642062353 • Serre's problem on projective modules, T. Y. Lam, 2006, Berlin, Springer, 1 vol. (XXI-401 p.), Springer monographs in mathematics, 3-540-23317-2 |
| 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 |
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| Item Description: | Description d'après consultation du 22 avril 2011 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Bibliography: | Bibliogr. p. [363]-393. Index |
| ISBN: | 9783540345756 |
| ISSN: | 2196-9922 |
| Access: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |