H. Charalambous, K. Karagiannis, Sotiris Karanikolopoulos, A. Kontogeorgis
{"title":"Syzygies of ideals of polynomial rings over principal ideal domains","authors":"H. Charalambous, K. Karagiannis, Sotiris Karanikolopoulos, A. Kontogeorgis","doi":"10.1145/3373207.3404046","DOIUrl":null,"url":null,"abstract":"We study computational aspects of syzygies of graded modules over polynomial rings R[w1, ..., wg] when the base R is a discrete valuation ring. In particular, we use the torsion of their syzygies over R to provide a formula which describes the behavior of the Betti numbers when changing the base to the residue field or the fraction field of R. Our work is motivated by the deformation theory of curves.","PeriodicalId":186699,"journal":{"name":"Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation","volume":"64 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3373207.3404046","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We study computational aspects of syzygies of graded modules over polynomial rings R[w1, ..., wg] when the base R is a discrete valuation ring. In particular, we use the torsion of their syzygies over R to provide a formula which describes the behavior of the Betti numbers when changing the base to the residue field or the fraction field of R. Our work is motivated by the deformation theory of curves.
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