On the canonical element conjecture

Dutta, Sankar P.

doi:10.1090/S0002-9947-1987-0869233-2

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

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On the canonical element conjecture
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by Sankar P. Dutta PDF

Trans. Amer. Math. Soc. 299 (1987), 803-811 Request permission

Abstract:

The canonical element conjecture is proved in the following two cases: (i) depth $A = \dim A - 1$, $H_m^{n - 1}(A)$ is decomposable; (ii) depth $A = \dim A - 1$, $H_m^{n - 1}{(A)^ \vee }$ is cyclic. The equivalence of the C.E.C. and the improved new intersection theorem is also established.

References

Melvin Hochster, Canonical elements in local cohomology modules and the direct summand conjecture, J. Algebra 84 (1983), no. 2, 503–553. MR 723406, DOI 10.1016/0021-8693(83)90092-3

The equivalence of two forms of the canonical element conjecture