This book presents recent developments and applications of Grothendieck’s local cohomology theory. The book is an expanded and updated version of two minicourse lectures and surveys, delivered at a workshop at CIMAT (Mexico) in 1999. The first lectures, on local cohomology and equivariant theory, are by J. Greenlees; the second, on local cohomology and duality, are by J. Lipman. M. Brodman then surveys recent results on cohomology of projective schemes, and G. Lyubeznik the development in local cohomology in the 1990s. H. Tsai and A. Leykin deal with algorithmic aspects of local cohomology via D-modules, E. Miller and K. Yanagawa discuss local cohomology over graded rings, A. Singh deals with associated primes of the local cohomology module, and I-Chiau Huang with applications to combinatorial analysis.
This book will be of considerable interest to algebraists and geometers, and also to topologists and specialists working in combinatorics and the theory of D-modules.