Cohen-macaulay modules

  • Melvin Hochster
Conference paper
First Online:
Part of the Lecture Notes in Mathematics book series (LNM, volume 311)

Abstract

The object of this paper is to discuss the conjecture, which will be abbreviated (E), that every complete local ring of dimension n possesses a finitely generated module of depth n. It is noted that several conjectures which have been open for some time follow from (E), and the connection of (E) with Serre's conjecture on multiplicities over regular local rings is discussed. In fact Serre's conjecture is proved for dimension ≤ 4 using the ideas under consideration.

A number of proofs of (E) for the two-dimensional case are given, and some possible methods for handling the general case are discussed. One of these is proposed as particularly worthy of study and is applied to an interesting class of examples in dimension 3 to obtain modules of depth 3. These examples do not yield easily to other techniques.

Keywords

Exact Sequence Local Ring Betti Number Projective Dimension Ring Homomorphism 
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Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • Melvin Hochster
    • 1
  1. 1.University of MinnesotaMinneapolis

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