Twenty-Four Hours of Local Cohomology

AvSrikanth B. Iyengar,Graham J. Leuschke

Häftad, Engelska, 2007

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2007-01-01
Format:Häftad
Språk:Engelska
Serie:Graduate Studies in Mathematics
Antal sidor:282
Förlag:American Mathematical Society
ISBN:9781470471590

Utforska kategorier

Matematik inom Naturvetenskap och teknik
Algebra inom Naturvetenskap och teknik

Mer om författaren

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.

Recensioner i media

"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

Innehållsförteckning

Basic notionsCohomologyResolutions and derived functorsLimitsGradings, filtrations, and Grobner basesComplexes from a sequence of ring elementsLocal cohomologyAuslander-Buchsbaum formula and global dimensionDepth and cohomological dimensionCohen-Macaulay ringsGorenstein ringsConnections with sheaf cohomologyProjective varietiesThe Hartshorne-Lichtenbaum vanishing theoremConnectednessPolyhedral applications$D$-modulesLocal duality revisitedDe Rham cohomologyLocal cohomology over semigroup ringsThe Frobenius endomorphismCurious examplesAlgorithmic aspects of local cohomologyHolonomic rank and hypergeometric systemsInjective modules and Matlis dualityBibliographyIndex

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