{"title":"Cohen-Macaulay模块的分层分辨率","authors":"D. Eisenbud, I. Peeva","doi":"10.4171/jems/1024","DOIUrl":null,"url":null,"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 = 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].","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2020-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Layered resolutions of Cohen–Macaulay modules\",\"authors\":\"D. Eisenbud, I. Peeva\",\"doi\":\"10.4171/jems/1024\",\"DOIUrl\":null,\"url\":null,\"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 = 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].\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2020-11-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/jems/1024\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/jems/1024","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
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].