Let be a Gorenstein local ring and suppose that is a finitely generated Cohen–Macaulay -module of codimension . Given a regular sequence in the annihilator of we set and construct layered -free and -free resolutions of . The construction inductively reduces the problem to the case of a Cohen–Macaulay module of codimension and leads to the inductive construction of a higher matrix factorization for . In the case where is a sufficiently high -syzygy of some module of finite projective dimension over , 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. 845–867DOI 10.4171/JEMS/1024