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Journal of the London Mathematical Society 1997 56(1):49-63; doi:10.1112/S0024610797005292
© 1997 by London Mathematical Society
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© The London Mathematical Society

Dualizing Complex and the Canonical Element Conjecture II

S. P. Dutta

Department of Mathematics, University of Illinois 1409 West Green Street, Urbana 61801, USA. E-mail: dutta{at}math.uiuc.edu

Received 5 October 1994. Revision received 6 June 1995.

In this paper we continue our study of the Canonical Element Conjecture (henceforth C.E.C.) via the dualizing complex. Throughout the work (A, m, k) will denote a noetherian complete local ring A of dimension n, m its maximal ideal and k=A/m. Since A is complete, we can find a complete local Gorenstein ring (R, mR, k) (complete intersection) such that dim R=dim A and A=R/I. Let {Omega} denote the canonical module of A, that is, {Omega}=HomR (A, R), which may be identified with the annihilator of I in R, an ideal of R. When A is a domain, we change notation and denote I by P; in this case P is a height 0 prime ideal of R.


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