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Paper   IPM / M / 726
School of Mathematics
  Title:   Cohomological dimension of certain algebraic varieties
1.  K. Divaani-Aazar
2.  R. Naghipour
3.  M. Tousi
  Status:   Published
  Journal: Proc. Amer. Math. Soc.
  No.:  12
  Vol.:  130
  Year:  2002
  Pages:   3537-3544
  Supported by:  IPM
Let \fraka be an ideal of a commutative Noetherian ring R. For finitely generated R-modules M and N with Supp N ⊆ Supp M, it is shown that cd (\fraka,N) ≤ cd (\fraka,M). Let N be a finitely generated module over a local ring (R,\frak m) such that MinRN = AsshRN. Using the above result and the notion of connectedness dimension, it is proved that cd (\fraka,N) ≥ dimNc(N/\fraka N)−1. Here c(N) denotes the connectedness dimension of the topological space Supp N. Finally, as a consequence of this inequality, two previously known generalizations of Faltings' connectedness theorem are improved.

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