Overview

This book is aimed to provide an introduction to local cohomology which takes cognizance of the breadth of its interactions with other areas of mathematics. It covers topics such as the number of defining equations of algebraic sets, connectedness properties of algebraic sets, connections to sheaf cohomology and to de Rham cohomology, Grobner bases in the commutative setting as well as for $D$-modules, the Frobenius morphism and characteristic $p$ methods, finiteness properties of local cohomology modules, semigroup rings and polyhedral geometry, and hypergeometric systems arising from semigroups. 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.

Full Product Details

Author:   Srikanth B. Iyengar ,  Graham J. Leuschke ,  Anton Leykin ,  Claudia S. Miller
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Edition:   UK ed.
Volume:   No. 87
Weight:   0.709kg
ISBN:  

9780821841266

ISBN 10:   0821841262
Pages:   282
Publication Date:   30 November 2007
Audience:   College/higher education ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Awaiting stock  
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Table of 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.

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