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.
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This lecture provides a summary of basic notions concerning algebraic sets, i.e., solution sets of polynomial equations. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
filtered posets, holonomic rank, canonical module, local cohomology modules, flasque sheaves, arithmetic rank, homogeneous maximal ideal, local cohornology, minimal injective resolution, punctured spectrum, polyhedral nature, exhaustive filtration, local duality theorem, affine semigroup, prime avoidance, finite projective dimension, height theorem, cohomological degrees, maximal essential extension, regular local ring, dualizing complex, minimal free resolution, semigroup ring, simplicial polytope, injective hull Key Phrases - Capitalized Phrases (CAPs): (learn more)
Cech-de Rham, Using Exercise, Using Theorem, I-diagrams of R-modules Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This lecture provides a summary of basic notions concerning algebraic sets, i.e., solution sets of polynomial equations. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
filtered posets, holonomic rank, canonical module, local cohomology modules, flasque sheaves, arithmetic rank, homogeneous maximal ideal, local cohornology, minimal injective resolution, punctured spectrum, polyhedral nature, exhaustive filtration, local duality theorem, affine semigroup, prime avoidance, finite projective dimension, height theorem, cohomological degrees, maximal essential extension, regular local ring, dualizing complex, minimal free resolution, semigroup ring, simplicial polytope, injective hull Key Phrases - Capitalized Phrases (CAPs): (learn more)
Cech-de Rham, Using Exercise, Using Theorem, I-diagrams of R-modules Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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