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Local Cohomology : An Algebraic Introduction with Geometric Applications

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Title: Local Cohomology : An Algebraic Introduction with Geometric Applications
Description: 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 Theorem 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 300 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.
Authors: M. P. Brodmann, R. Y. Sharp
Resource Type: eBook.
Subjects: Algebra, Homological, Sheaf theory, Commutative algebra
Categories: MATHEMATICS / Algebra / Intermediate
Database: eBook Collection (EBSCOhost)
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  – Type: ebook-pdf
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  Availability: 0
Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 494777
RelevancyScore: 1051
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 1050.81640625
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  Label: Title
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  Data: Local Cohomology : An Algebraic Introduction with Geometric Applications
– Name: Abstract
  Label: Description
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  Data: 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 Theorem 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 300 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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  Data: <searchLink fieldCode="DE" term="%22Algebra%2C+Homological%22">Algebra, Homological</searchLink><br /><searchLink fieldCode="DE" term="%22Sheaf+theory%22">Sheaf theory</searchLink><br /><searchLink fieldCode="DE" term="%22Commutative+algebra%22">Commutative algebra</searchLink>
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        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Algebra, Homological
        Type: general
      – SubjectFull: Sheaf theory
        Type: general
      – SubjectFull: Commutative algebra
        Type: general
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      – TitleFull: Local Cohomology : An Algebraic Introduction with Geometric Applications
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            – D: 01
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              Type: published
              Y: 2013
            – D: 04
              M: 02
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              Y: 2014
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              Value: 9781139775762
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              Value: 00136
          Titles:
            – TitleFull: Local Cohomology : An Algebraic Introduction with Geometric Applications
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