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The Resource Completion, Čech and Local Homology and Cohomology : Interactions Between Them, by Peter Schenzel, Anne-Marie Simon, (electronic resource)

Completion, Čech and Local Homology and Cohomology : Interactions Between Them, by Peter Schenzel, Anne-Marie Simon, (electronic resource)

Label
Completion, Čech and Local Homology and Cohomology : Interactions Between Them
Title
Completion, Čech and Local Homology and Cohomology
Title remainder
Interactions Between Them
Statement of responsibility
by Peter Schenzel, Anne-Marie Simon
Creator
Contributor
Author
Author
Subject
Language
eng
Summary
The aim of the present monograph is a thorough study of the adic-completion, its left derived functors and their relations to the local cohomology functors, as well as several completeness criteria, related questions and various dualities formulas. A basic construction is the Čech complex with respect to a system of elements and its free resolution. The study of its homology and cohomology will play a crucial role in order to understand left derived functors of completion and right derived functors of torsion. This is useful for the extension and refinement of results known for modules to unbounded complexes in the more general setting of not necessarily Noetherian rings. The book is divided into three parts. The first one is devoted to modules, where the adic-completion functor is presented in full details with generalizations of some previous completeness criteria for modules. Part II is devoted to the study of complexes. Part III is mainly concerned with duality, starting with those between completion and torsion and leading to new aspects of various dualizing complexes. The Appendix covers various additional and complementary aspects of the previous investigations and also provides examples showing the necessity of the assumptions. The book is directed to readers interested in recent progress in Homological and Commutative Algebra. Necessary prerequisites include some knowledge of Commutative Algebra and a familiarity with basic Homological Algebra. The book could be used as base for seminars with graduate students interested in Homological Algebra with a view towards recent research.--
Member of
Assigning source
Provided by publisher
http://library.link/vocab/creatorName
Schenzel, Peter
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • 93l4ixM23Hs
  • eux4LvvU97M
Image bit depth
0
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Simon, Anne-Marie
Series statement
  • Springer Monographs in Mathematics,
  • Springer eBooks
  • Springer eBooks.
http://library.link/vocab/subjectName
Algebra
Label
Completion, Čech and Local Homology and Cohomology : Interactions Between Them, by Peter Schenzel, Anne-Marie Simon, (electronic resource)
Link
http://ezproxy.eui.eu/login?url=https://doi.org/10.1007/978-3-319-96517-8
Instantiates
Publication
Antecedent source
mixed
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
Part I: Modules,- 1. Preliminaries and auxiliary results -- 2. Adic topology and completion -- 3. Ext-Tor vanishing and completeness criteria -- PartII: Complexes -- 4. Homological Preliminaries -- 5. Koszul complexes, depth and codepth -- 6. Čech complexes, Čech homology and cohomology -- 7. Local cohomology and local homology -- 8. The formal power series Koszul complex -- 9. Complements and Applications -- Part III: Duality -- 10. Čech and local duality -- 11. Dualizing complexes -- 12. Local duality with dualizing complexes and other dualities -- Appendix -- References -- Notation -- Subject Index
Control code
978-3-319-96517-8
Dimensions
unknown
Extent
1 online resource (XVII, 346 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319965178
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1052766500
Label
Completion, Čech and Local Homology and Cohomology : Interactions Between Them, by Peter Schenzel, Anne-Marie Simon, (electronic resource)
Link
http://ezproxy.eui.eu/login?url=https://doi.org/10.1007/978-3-319-96517-8
Publication
Antecedent source
mixed
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
Part I: Modules,- 1. Preliminaries and auxiliary results -- 2. Adic topology and completion -- 3. Ext-Tor vanishing and completeness criteria -- PartII: Complexes -- 4. Homological Preliminaries -- 5. Koszul complexes, depth and codepth -- 6. Čech complexes, Čech homology and cohomology -- 7. Local cohomology and local homology -- 8. The formal power series Koszul complex -- 9. Complements and Applications -- Part III: Duality -- 10. Čech and local duality -- 11. Dualizing complexes -- 12. Local duality with dualizing complexes and other dualities -- Appendix -- References -- Notation -- Subject Index
Control code
978-3-319-96517-8
Dimensions
unknown
Extent
1 online resource (XVII, 346 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319965178
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1052766500

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