Some dimension 3 cases of the canonical element conjecture

Huneke, Craig; Koh, Jee

doi:10.1090/S0002-9939-1986-0857928-0

Some dimension $3$ cases of the canonical element conjecture
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by Craig Huneke and Jee Koh PDF

Proc. Amer. Math. Soc. 98 (1986), 394-398 Request permission

Abstract:

The Canonical Element Conjecture holds for those $3$-dimensional local rings of depth 2 whose second local cohomology module is a finite direct sum of cyclic modules, and for those $3$-dimensional local rings whose second local cohomology module is cyclic.

References

Markus P. Brodmann, Finiteness of ideal transforms, J. Algebra 63 (1980), no. 1, 162–185. MR 568570, DOI 10.1016/0021-8693(80)90031-9
Winfried Bruns, The Eisenbud-Evans generalized principal ideal theorem and determinantal ideals, Proc. Amer. Math. Soc. 83 (1981), no. 1, 19–24. MR 619972, DOI 10.1090/S0002-9939-1981-0619972-3
David Eisenbud and E. Graham Evans Jr., A generalized principal ideal theorem, Nagoya Math. J. 62 (1976), 41–53. MR 409440
Robin Hartshorne, Local cohomology, Lecture Notes in Mathematics, No. 41, Springer-Verlag, Berlin-New York, 1967. A seminar given by A. Grothendieck, Harvard University, Fall, 1961. MR 0224620
Melvin Hochster, Topics in the homological theory of modules over commutative rings, Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 24, Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, Providence, R.I., 1975. Expository lectures from the CBMS Regional Conference held at the University of Nebraska, Lincoln, Neb., June 24–28, 1974. MR 0371879
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

Degree

extensions of an unramified regular local ring of mixed characteristic

The equivalence of two forms of the Canonical Element Conjecture