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Equidimensional local rings with finite Cousin cohomology modules

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It is shown that any equidimensional local ring which has finite Cousin cohomology modules with respect to the dimension filtration has a uniform local cohomological annihilator and is universally catenary.

Abstract

It is shown that any equidimensional local ring which has finite Cousin cohomology modules with respect to the dimension filtration has a uniform local cohomological annihilator and is universally catenary.

참고문헌 (14)

  1. M. P. Brodmann, "Local Cohomology: An Algebraic Introduction with Geometric Applications" (1998), Cambridge University Press
  2. W. Bruns, "Cohen-Macaulay Rings" (1993), Cambridge University Press
  3. M. T. Dibaei, "A study of Cousin complexes through the dualizing complexes", Comm. Algebra, 33(1), pp.119~132 (2005)
  4. M. T. Dibaei, "Modules with finite Cousin cohomologies have uniform local cohomological annihilators", J. Algebra, 319(8), pp.3291~3300 (2008)
  5. M. T. Dibaei, "The structure of dualizing complex for a ring which is (S2)", J. Math. Kyoto Univ, 38(3), pp.503~516 (1998)
  6. M. T. Dibaei, "A generalization of the dualizing complex structure and its applications", J. Pure Appl. Algebra, 155(1), pp.17~28 (2001)
  7. 64, "Residues and Duality, Lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963", pp.1966, R. Hartshorne
  8. T. Kawasaki, "Finiteness of Cousin cohomologies", Trans. Amer. Math. Soc, 360(5), pp.2709~2739 (2008)
  9. J. Lipman, "Variance and duality for Cousin complexes on formal schemes", pp.3~133 (2005), Amer. Math. Soc.
  10. J. J. Rotman, "An Introduction to Homological Algebra" (1979), Academic Press, Inc.
  11. R. Y. Sharp, "The Cousin complex for a module over a commutative Noetherian ring", Math. Z, 112, pp.340~356 (1969)
  12. R. Y. Sharp, "Gorenstein modules", Math. Z, 115, pp.117~139 (1970)
  13. R. Y. Sharp, "A Cousin complex characterization of balanced big Cohen-Macaulay modules", Quart. J. Math. Oxford Ser. (2), 33(132), pp.471~485 (1982)
  14. C. Zhou, "Uniform annihilators of local cohomology", J. Algebra, 305(1), pp.585~602 (2006)

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