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Cohomological annihilators

Published online by Cambridge University Press:  24 October 2008

Peter Schenzel
Peter Schenzel
Affiliation:
Martin-Luther-Universität Halle-Wittenberg, DDR - 4010, Halle
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Extract

The local cohomology theory introduced by Grothendieck(1) is a useful tool for attacking problems in commutative algebra and algebraic geometry. Let A denote a local ring with its unique maximal ideal m. For an ideal I ⊂ A and a finitely generated A-module M we consider the local cohomology modules HiI (M), i є ℤ, of M with respect to I, see Grothendieck(1) for the definition. In particular, the vanishing resp. non-vanishing of the local cohomology modules is of a special interest. For more subtle considerations it is necessary to study the cohomological annihilators, i.e. aiI(M): = AnnΔHiI(M), iєℤ. In the case of the maximal ideal I = m these ideals were used by Roberts (6) to prove the ‘New Intersection Theorem’ for local rings of prime characteristic. Furthermore, we used this notion (7) in order to show the amiability of local rings possessing a dualizing complex. Note that the amiability of a system of parameters is the key step for Hochster's construction of big Cohen-Macaulay modules for local rings of prime characteristic, see Hochster(3) and (4).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 91 , Issue 3 , May 1982 , pp. 345 - 350
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

REFERENCES

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