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Twenty-Four Hours of Local Cohomology
About this Title
Srikanth B. Iyengar, University of Nebraska, Lincoln, NE, Graham J. Leuschke, Syracuse University, Syracuse, NY, Anton Leykin, Institute for Mathematics and Its Applications, Syracuse, NY, Claudia Miller, Syracuse University, Syracuse, NY, Ezra Miller, University of Minnesota, Minneapolis, MN, Anurag K. Singh, University of Utah, Salt Lake City, UT and Uli Walther, Purdue University, West Lafayette, IN
Publication: Graduate Studies in Mathematics
Publication Year:
2007; Volume 87
ISBNs: 978-0-8218-4126-6 (print); 978-1-4704-2117-5 (online)
DOI: https://doi.org/10.1090/gsm/087
MathSciNet review: MR2355715
MSC: Primary 13D45; Secondary 14B15, 55N30
ReadershipTable of Contents
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Front/Back Matter
Chapters
- Lecture 1. Basic notions
- Lecture 2. Cohomology
- Lecture 3. Resolutions and derived functors
- Lecture 4. Limits
- Lecture 5. Gradings, filtrations, and Gröbner bases
- Lecture 6. Complexes from a sequence of ring elements
- Lecture 7. Local cohomology
- Lecture 8. Auslander-Buchsbaum formula and global dimension
- Lecture 9. Depth and cohomological dimension
- Lecture 10. Cohen-Macaulay rings
- Lecture 11. Gorenstein rings
- Lecture 12. Connections with sheaf cohomology
- Lecture 13. Projective varieties
- Lecture 14. The Hartshorne-Lichtenbaum vanishing theorem
- Lecture 15. Connectedness
- Lecture 16. Polyhedral applications
- Lecture 17. $D$-modules
- Lecture 18. Local duality revisited
- Lecture 19. De Rham cohomology
- Lecture 20. Local cohomology over semigroup rings
- Lecture 21. The Frobenius endomorphism
- Lecture 22. Curious examples
- Lecture 23. Algorithmic aspects of local cohomology
- Lecture 24. Holonomic rank and hypergeometric systems
- Appendix. Injective modules and Matlis duality