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Twenty-Four Hours of Local Cohomology

Srikanth B Iyengar, Graham J Leusch ke, Anton LeyKin, Claudia Miller, Ezra Miller, Anurag K Singh, Uli Walther

₹ 1845

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Imprint	American Mathematical Society
Year of Publishing	2011
Number of pages	304
ISBN	9780821868836
Format	Paperback
Language	English
Dimensions	180 x 240 mm
Series	Indian Editions of AMS Titles
Territorial Rights	India,Nepal,Bhutan,Bangladesh,Sri Lanka,Maldives,Pakistan
Catalogue(s)	Mathematics

the Book
the Author(s)
Table of Contents

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, Gröbner 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.

The Author(s)

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, and Uli Walther, Purdue University, West Lafayette, IN

Table of Contents

Preface
Introduction
Lecture 1. Basic Notions
Lecture 2. Cohomology
Lecture 3. Resolutions and Derived Functors
Lecture 4. Limits
Lecture 5. Gradings, Filtrations, and Grobner 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
Bibliography
Index

Twenty-Four Hours of Local Cohomology

Srikanth B Iyengar, Graham J Leusch ke, Anton LeyKin, Claudia Miller, Ezra Miller, Anurag K Singh, Uli Walther

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