Ascent of finite Cohen-Macaulay type

Joint work with Roger Wiegand.


In 1987 F.-O. Schreyer conjectured that a local ring has finite Cohen-Macaulay type if and only if the completion has finite Cohen-Macaulay type. We prove the conjecture for excellent Cohen-Macaulay local rings and also show by example that it can fail in general.

This was the first paper I wrote, and it’s joint work with Roger Wiegand. Learning to write a paper (which I must admit I’m still doing) is incredibly difficult, and this one took me a very long time. I’m quite proud of how it turned out, though. One bit I particularly like is the ephemeral concept of “finite syzygy type”, which immediately turns out to be the same thing as “finite Cohen–Macaulay type” for CM rings. One of these days I’ll come back to this idea and see how badly it fails for non-CM rings (assumption: infinitely badly).

Bibtex code:

 @article {MR1764587,
    AUTHOR = {Leuschke, Graham and Wiegand, Roger},
     TITLE = {Ascent of finite {C}ohen-{M}acaulay type},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {228},
      YEAR = {2000},
    NUMBER = {2},
     PAGES = {674–681},
      ISSN = {0021-8693},
     CODEN = {JALGA4},
   MRCLASS = {13H10 (13C14)},
  MRNUMBER = {MR1764587 (2001k:13035)},
 MRREVIEWER = {Sunsook Noh},