Foundations of Grothendieck duality for diagrams of schemes
The first part written by Joseph Lipman, accessible to mid-level graduate students, is a full exposition of the abstract foundations of Grothendieck duality theory for schemes (twisted inverse image, tor-independent base change,...), in part without noetherian hypotheses, and with some refinements f...
Guardado en:
| Autores principales: | , |
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| Formato: | Livre numérique |
| Lenguaje: | Anglais |
| Publicado: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Edición: | 1st ed. 2009. |
| Colección: | Lecture Notes in Mathematics
1960 |
| Materias: | |
| Acceso en línea: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Description d'apès consultation du 23 janvier 2012 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Foundations of Grothendieck duality for diagrams of schemes, Joseph Lipman, Mitsuyasu Hashimoto, Berlin, Springer, 2009, 1 vol. (X-478 p.), Lecture notes in mathematics, 978-3-540-85419-7 • Foundations of Grothendieck Duality for Diagrams of Schemes, Texte imprimé, 9783540854432 • Foundations of Grothendieck duality for diagrams of schemes, Joseph Lipman, Mitsuyasu Hashimoto, Berlin, Springer, 2009, 1 vol. (X-478 p.), Lecture notes in mathematics, 978-3-540-85419-7 |
| Sumario: | The first part written by Joseph Lipman, accessible to mid-level graduate students, is a full exposition of the abstract foundations of Grothendieck duality theory for schemes (twisted inverse image, tor-independent base change,...), in part without noetherian hypotheses, and with some refinements for maps of finite tor-dimension. The ground is prepared by a lengthy treatment of the rich formalism of relations among the derived functors, for unbounded complexes over ringed spaces, of the sheaf functors tensor, hom, direct and inverse image. Included are enhancements, for quasi-compact quasi-separated schemes, of classical results such as the projection and Künneth isomorphisms. In the second part, written independently by Mitsuyasu Hashimoto, the theory is extended to the context of diagrams of schemes. This includes, as a special case, an equivariant theory for schemes with group actions. In particular, after various basic operations on sheaves such as (derived) direct images and inverse images are set up, Grothendieck duality and flat base change for diagrams of schemes are proved. Also, dualizing complexes are studied in this context. As an application to group actions, we generalize Watanabe's theorem on the Gorenstein property of invariant subrings. |
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| Notas: | Description d'apès consultation du 23 janvier 2012 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ISBN: | 9783540854203 |
| ISSN: | 1617-9692 |
| Acceso: | 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 |