Local cohomology : an algebraic introduction with geometric applications / M.P. Brodmann, R.Y. Sharp.

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"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 quas...

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Bibliographic Details
Main Author: Brodmann, M. P. (Markus P.), 1945-
Other Authors: Sharp, R. Y.
Language:English
Published: Cambridge ; New York : Cambridge University Press, 2013.
Edition:Second edition.
Series:Cambridge studies in advanced mathematics ; 136.
Subjects:
Algebra, Homological.
Physical Description:xxii, 491 pages : illustrations ; 24 cm.
Format: Book
Contents:
  • The local cohomology functors
  • Torsion modules and ideal transforms
  • The Mayer-Vietoris sequence
  • Change of rings
  • Other approaches
  • Fundamental vanishing theorems
  • Artinian local cohomology modules
  • The Lichtenbaum-Hartshorne Theorem
  • The Annihilator and Finiteness Theorems
  • Matlis duality
  • Local duality
  • Canonical modules
  • Foundations in the graded case
  • Graded versions of basic theorems
  • Links with projective varieties
  • Castelnuovo regularity
  • Hilbert polynomials
  • Applications to reductions of ideals
  • Connectivity in algebraic varieties
  • Links with sheaf cohomology.