Twenty-Four Hours of Local Cohomology

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.

• 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

"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