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- Title
Layered resolutions of Cohen-Macaulay modules.
- Authors
Eisenbud, David; Peeva, Irena
- Abstract
Let S be a Gorenstein local ring and suppose that M is a finitely generated Cohen-Macaulay S-module of codimension c. Given a regular sequence f1.... fc in the annihilator of M we set R D S=.f1.... fc/and construct layered S-free and R-free resolutions of M. The construction inductively reduces the problem to the case of a Cohen-Macaulay module of codimension c - 1 and leads to the inductive construction of a higher matrix factorization for M. In the case where M is a sufficiently high R-syzygy of some module of finite projective dimension over S, 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.
- Subjects
COHEN-Macaulay modules; FACTORIZATION; ALGEBRAIC geometry; APPROXIMATION theory; SYZYGIES (Mathematics)
- Publication
Journal of the European Mathematical Society (EMS Publishing), 2021, Vol 23, Issue 3, p845
- ISSN
1435-9855
- Publication type
Article
- DOI
10.4171/JEMS/1024