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Research/Mixed-Characteristic Hypersurfaces of Finite Cohen-Macaulay Type

Abstract:

We define the “mixed ADE singularities”, which are generalizations of the ADE plane curve singularities to the case of mixed characteristic. The ADE plane curve singularities are precisely the equicharacteristic plane curve singularities of finite Cohen-Macaulay type; we show that the mixed ADE singularities also have finite Cohen-Macaulay type.

Notes:

This was the final third of my dissertation. It’s one of those classic things that end up in dissertations because nobody but a graduate student would ever spend the time checking the details. There’s very little of interest here for most people, except perhaps the statement of the main theorem. For me personally, though, it was a great learning experience, if only because I had to work carefully through the matrix operations that are hinted at in Yoshino’s book.

Bibtex code:

 @article {MR1874543,
    AUTHOR = {Leuschke, Graham J.},
     TITLE = {Mixed characteristic hypersurfaces of finite
              {C}ohen-{M}acaulay type},
   JOURNAL = {J. Pure Appl. Algebra},
  FJOURNAL = {Journal of Pure and Applied Algebra},
    VOLUME = {167},
      YEAR = {2002},
    NUMBER = {2–3},
     PAGES = {225—257},
      ISSN = {0022–4049},
     CODEN = {JPAAA2},
   MRCLASS = {13C14 (13H10 14B05)},
  MRNUMBER = {MR1874543 (2002k:13019)},
 MRREVIEWER = {Marcel Morales},
 }

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