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 Miller
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
ISBN:  

9781470471590

ISBN 10:   1470471590
Pages:   282
Publication Date:   01 January 2007
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

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 modules and Matlis duality Bibliography Index

Reviews

It's all terrific stuff. I hope this book will succeed in bringing many young mathematicians to love cohomology, too, and then to go on from there. -MAA Reviews This book is an excellent text on local cohomology and complements well the existing sources. It will surely become a standard reference on this theory. -Mathematical Reviews

"It's all terrific stuff. I hope this book will succeed in bringing many young mathematicians to love cohomology, too, and then to go on from there."" —MAA Reviews ""This book is an excellent text on local cohomology and complements well the existing sources. It will surely become a standard reference on this theory."" —Mathematical Reviews"

Author Information

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.

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions