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Dualizing complexes for commutative Noetherian rings

Published online by Cambridge University Press:  24 October 2008

Rodney Y. Sharp
Rodney Y. Sharp
Affiliation:
University of Sheffield
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Extract

The theory of dualizing complexes of Grothendieck and Hartshorne ((5), chapter v) has turned out to be a useful tool even in commutative algebra. For instance, Peskine and Szpiro used dualizing complexes in their (partial) solution of Bass's conjecture concerning finitely-generated (f.-g.) modules of finite injective dimension over a Noetherian local ring ((7), chapitre I, §5); and the present author first obtained the results in (9) by using dualizing complexes.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 78 , Issue 3 , November 1975 , pp. 369 - 386
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

REFERENCES

(1)Atiyah, M. F. and MacDonald, L. G.Introduction to commutative algebra (Addison Wesley, 1969).Google Scholar
(2)Bass, H.On the ubiquity of Gorenstein rings. Math. Z. 82 (1963), 8–28.CrossRefGoogle Scholar
(3)Cartan, H. and Eilenberg, S.Homological algebra (Princeton University Press, 1956).Google Scholar
(4)Douglas, A. J.An elementary derivation of certain homological inequalities. Mathematika 10 (1963), 114–124.CrossRefGoogle Scholar
(5)Hartshorne, R.Residues and duality (Springer Lecture Notes in Mathematics, no. 20, 1966).CrossRefGoogle Scholar
(6)Northcott, D. G.An introduction to homological algebra (Cambridge University Press, 1962).Google Scholar
(7)Peskine, C. and Szpiro, L.Dimension projective finie et cohomologie locale. Inst. Hautes Études Sci. Publ. Math. 42 (1973), 323–395.CrossRefGoogle Scholar
(8)Serre, J.-P.Algèbre locale: multiplicités (Springer Lecture Notes in Mathematics, no. 11, 1965).Google Scholar
(9)Sharp, R. Y.Finitely generated modules of finite injective dimension over certain Cohen–Macaulay rings. Proc. London Math. Soc. (3) 25 (1972), 303–328.CrossRefGoogle Scholar
(10)Swan, R. G.Algebraic K-theory (Springer Lecture Notes in Mathematics, no. 76, 1968).CrossRefGoogle Scholar