On the Use of Local Cohomology in Algebra and Geometry
نویسندگان
چکیده
Introduction 2 1. A Guide to Duality 3 1.1. Local Duality 3 1.2. Dualizing Complexes and Some Vanishing Theorems 10 1.3. Cohomological Annihilators 17 2. A Few Applications of Local Cohomology 21 2.1. On Ideal Topologies 21 2.2. On Ideal Transforms 25 2.3. Asymptotic Prime Divisors 28 2.4. The Lichtenbaum-Hartshorne Vanishing Theorem 35 2.5. Connectedness results 37 3. Local Cohomology and Syzygies 40 3.1. Local cohomology and Tor’s 40 3.2. Estimates of Betti numbers 45 3.3. Castelnuovo-Mumford regularity 46 3.4. The local Green modules 51 References 55
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