{"product_id":"twentyfour-hours-of-local-cohomology-9781470471590","title":"TwentyFour Hours of Local Cohomology","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eIt'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.\" —\u003cem\u003eMAA Reviews\u003c\/em\u003e\u003cbr\u003e\u003cbr\u003e\"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.\" —\u003cem\u003eMathematical Reviews \u003c\/em\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cul\u003e\n\u003cli\u003eBasic notions\u003c\/li\u003e\n\u003cli\u003eCohomology\u003c\/li\u003e\n\u003cli\u003eResolutions and derived functors\u003c\/li\u003e\n\u003cli\u003eLimits\u003c\/li\u003e\n\u003cli\u003eGradings, filtrations, and Grobner bases\u003c\/li\u003e\n\u003cli\u003eComplexes from a sequence of ring elements\u003c\/li\u003e\n\u003cli\u003eLocal cohomology\u003c\/li\u003e\n\u003cli\u003eAuslander-Buchsbaum formula and global dimension\u003c\/li\u003e\n\u003cli\u003eDepth and cohomological dimension\u003c\/li\u003e\n\u003cli\u003eCohen-Macaulay rings\u003c\/li\u003e\n\u003cli\u003eGorenstein rings\u003c\/li\u003e\n\u003cli\u003eConnections with sheaf cohomology\u003c\/li\u003e\n\u003cli\u003eProjective varieties\u003c\/li\u003e\n\u003cli\u003eThe Hartshorne-Lichtenbaum vanishing theorem\u003c\/li\u003e\n\u003cli\u003eConnectedness\u003c\/li\u003e\n\u003cli\u003ePolyhedral applications\u003c\/li\u003e\n\u003cli\u003e$D$-modules\u003c\/li\u003e\n\u003cli\u003eLocal duality revisited\u003c\/li\u003e\n\u003cli\u003eDe Rham cohomology\u003c\/li\u003e\n\u003cli\u003eLocal cohomology over semigroup rings\u003c\/li\u003e\n\u003cli\u003eThe Frobenius endomorphism\u003c\/li\u003e\n\u003cli\u003eCurious examples\u003c\/li\u003e\n\u003cli\u003eAlgorithmic aspects of local cohomology\u003c\/li\u003e\n\u003cli\u003eHolonomic rank and hypergeometric systems\u003c\/li\u003e\n\u003cli\u003eInjective modules and Matlis duality\u003c\/li\u003e\n\u003cli\u003eBibliography\u003c\/li\u003e\n\u003cli\u003eIndex\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"MP-AMM American Mathematical","offers":[{"title":"Default Title","offer_id":50046713790807,"sku":"9781470471590","price":71.1,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781470471590.jpg?v=1740272530","url":"https:\/\/bookcurl.com\/products\/twentyfour-hours-of-local-cohomology-9781470471590","provider":"Book Curl","version":"1.0","type":"link"}