JournalsjemsVol. 23, No. 3pp. 845–867

Layered resolutions of Cohen–Macaulay modules

  • David Eisenbud

    University of California, Berkeley and MSRI, USA
  • Irena Peeva

    Cornell University, Ithaca, USA
Layered resolutions of Cohen–Macaulay modules cover
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Abstract

Let SS be a Gorenstein local ring and suppose that MM is a finitely generated Cohen–Macaulay SS-module of codimension cc. Given a regular sequence f1,,fcf_1, \ldots, f_c in the annihilator of MM we set R=S/(f1,,fc)R = S/(f_1, \ldots, f_c) and construct layered SS-free and RR-free resolutions of MM. The construction inductively reduces the problem to the case of a Cohen–Macaulay module of codimension c1c-1 and leads to the inductive construction of a higher matrix factorization for MM. In the case where MM is a sufficiently high RR-syzygy of some module of finite projective dimension over SS, the layered resolutions are minimal and coincide with the resolutions defined from higher matrix factorizations we described in [EP]. Our results provide a characterization of all MCM modules over a complete intersection in terms of higher matrix factorizations.

Cite this article

David Eisenbud, Irena Peeva, Layered resolutions of Cohen–Macaulay modules. J. Eur. Math. Soc. 23 (2021), no. 3, pp. 845–867

DOI 10.4171/JEMS/1024