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Twenty-four hours of local cohomology

Author: Srikanth Iyengar
Publisher: Providence, R.I. : American Mathematical Society ; Oxford : Oxford University Press [distributor], 2008.
Series: Graduate studies in mathematics, v. 87.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
This is an introduction to local cohomology which takes cognizance of the breadth of its interactions with other areas of mathematics. The text covers topics such as the number of defining equations of algebraic sets, connectedness properties of algebraic sets, and connections to sheaf cohomology and to de Rham cohomology.
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Document Type: Book
All Authors / Contributors: Srikanth Iyengar
ISBN: 9780821841266 0821841262
OCLC Number: 182663716
Description: xviii, 282 pages ; 27 cm.
Contents: 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 moduels and Matlis duality Bibliography Index.
Series Title: Graduate studies in mathematics, v. 87.
Responsibility: Srikanth Iyengar [and others].

Abstract:

Aimed to provide an introduction to local cohomology, this book takes cognizance of the breadth of its interactions with other areas of mathematics. It begins with basic notions in geometry, sheaf  Read more...

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