Twenty-Four Hours of Local Cohomology
American Mathematical Society (Verlag)
978-1-4704-7159-0 (ISBN)
The book begins with basic notions in geometry, sheaf theory, and homological algebra leading to the definition and basic properties of local cohomology. Then it develops the theory in a number of different directions, and draws connections with topology, geometry, combinatorics, and algorithmic aspects of the subject.
Srikanth B. Iyengar, University of Nebraska, Lincoln, NE. Graham J. Leuschke, Syracuse University, NY. Anton Leykin, Institute for Mathematics and Its Applications, Syracuse, NY. Claudia Miller, Syracuse University, NY. Ezra Miller, University of Minnesota, Minneapolis, MN. Anurag K. Singh, University of Utah, Salt Lake City, UT. Uli Walther, Purdue University, West Lafayette, IN.
Basic notions
Cohomology
Resolutions and derived functors
Limits
Gradings, filtrations, and Grobner bases
Complexes from a sequence of ring elements
Local cohomology
Auslander-Buchsbaum formula and global dimension
Depth and cohomological dimension
Cohen-Macaulay rings
Gorenstein rings
Connections with sheaf cohomology
Projective varieties
The Hartshorne-Lichtenbaum vanishing theorem
Connectedness
Polyhedral applications
$D$-modules
Local duality revisited
De Rham cohomology
Local cohomology over semigroup rings
The Frobenius endomorphism
Curious examples
Algorithmic aspects of local cohomology
Holonomic rank and hypergeometric systems
Injective modules and Matlis duality
Bibliography
Index
Erscheinungsdatum | 18.11.2022 |
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Reihe/Serie | Graduate Studies in Mathematics |
Verlagsort | Providence |
Sprache | englisch |
Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
ISBN-10 | 1-4704-7159-0 / 1470471590 |
ISBN-13 | 978-1-4704-7159-0 / 9781470471590 |
Zustand | Neuware |
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