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 = 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 su ciently 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].

中文翻译：

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Cohen-Macaulay 模块的分层分辨率

设 S 是一个 Gorenstein 局部环，并假设 M 是一个有限生成的 Cohen-Macaulay S-模的余维 c。给定一个正则序列 f1, . . . , fc 在 M 的歼灭器中，我们设置 R = S/(f1, . . , fc) 并构造 M 的分层 S-free 和 R-free 分辨率。该构造将问题归纳地归结为一个 Cohen-Macaulay 模的 codimension c 1 的情况，并导致对 M 的更高矩阵分解的归纳构造。在 M 是 S 上某个有限投影维度模块的足够高的 R-syzygy 的情况下，分层分辨率是最小的，并且与我们在 [EP] 中描述的更高矩阵分解定义的分辨率一致。