need not be closed. We are able to conclude that the above-mentioned associativity formulae for local cohomology modules do not hold over all local rings. Local cohomology: An algebraic introduction with geometric Brodman and R. Y. Sharp, Cambridge University Press, , xv+ pp. Read “Local Cohomology An Algebraic Introduction with Geometric Applications” by M. P. with Geometric Applications ebook by M. P. Brodmann,R. Y. Sharp.
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See if you have enough points for this item. This second edition of a successful graduate text provides a careful and detailed algebraic introduction to Grothendieck’s local cohomology theory, including in multi-graded situations, and provides many illustrations of the theory in commutative algebra and in the geometry of quasi-affine and quasi-projective varieties.
Topics covered include Serre’s Affineness Criterion, the Lichtenbaum—Hartshorne Vanishing Theorem, Grothendieck’s Finiteness Cohmoology and Faltings’ Annihilator Theorem, local duality and canonical modules, the Fulton—Hansen Connectedness Theorem for projective varieties, and connections between local cohomology and both reductions of ideals and sheaf cohomology.
The book is designed for graduate students who have some experience of basic commutative algebra and homological algebra and also experts in commutative algebra and algebraic geometry. Over exercises are interspersed among the text; these range in difficulty from routine to challenging, and hints are provided for some of the more difficult ones.
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Brodmann , Sharp : On the dimension and multiplicity of local cohomology modules
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