Tate resolutions and {MCM} approximations
Tate resolutions and {MCM} approximations
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Tate 分辨率和 {MCM} 近似
DOI：
10.1090/conm/773/15531
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Frank-Olaf Schreyer
中科院分区：
文献类型：
--
作者：
David Eisenbud;Frank-Olaf Schreyer
设 M 是 Gorenstein 环 R= S/I 上余维 m 的有限生成的 Cohen-Macaulay 模，其中 S 是正则环。我们展示了如何使用 R 和 M 的 S 自由分辨率来形成准同构 & 从 M 的 R 自由分辨率到 M∨:= Ext (M, R) 的 R 自由分辨率的对偶。o 的映射锥是 M 的 Tate 分辨率，使我们能够计算 M 的最大 Cohen-Macaulay 近似。在 R 是 0 维局部且 M 是留数场的情况下，o 的公式变成了R 的底面概括了零维完全交集的底面的众所周知的公式。当 I⊂ J⊂ S 为正则序列生成的理想时，R-模 M= S/J 称为拟完全交集，Kustin 和 Şega 对 4 进行了详细研究。我们将它们的构建与最初由 Buchsbaum 和 Eisenbud 引入的“Eagon-Northcott”类复合物序列联系起来。
Let M be a finitely generated Cohen-Macaulay module of codi-mension m over a Gorenstein Ring R= S/I, where S is a regular ring. We show how to form a quasi-isomorphism & from an R-free resolution of M to the dual of an R-free resolution of M∨:= Ext (M, R) using the S-free resolutions of R and M. The mapping cone of o is then a Tate resolution of M, allowing us to compute the maximal Cohen-Macaulay approximation of M. In the case when R is 0-dimensional local, and M is the residue field, the formula for o becomes a formula for the socle of R generalizing a well-known formula for the socle of a zero-dimensional complete intersection. When I⊂ J⊂ S are ideals generated by regular sequences, the R-module M= S/J is called a quasi-complete intersection, and 4 was studied in detail by Kustin and Şega. We relate their construction to the sequence of" Eagon-Northcott"-like complexes originally introduced by Buchsbaum and Eisenbud.