Completion, Čech and Local Homology and Cohomology Interactions Between Them /

• Main Authors: Schenzel, Peter (Author, http://id.loc.gov/vocabulary/relators/aut), Simon, Anne-Marie (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: Springer Monographs in Mathematics,
• Subjects: Commutative algebra.; Commutative rings.; Commutative Rings and Algebras.

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 resp...

Table of 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.