{"title":"Mordell-Weil groups of quasi-elliptic or quasi-hyperelliptic surfaces","authors":"","doi":"10.1142/9789811215216_0010","DOIUrl":"https://doi.org/10.1142/9789811215216_0010","url":null,"abstract":"","PeriodicalId":249858,"journal":{"name":"Algebraic Surfaces in Positive Characteristics","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132783219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Quasi-elliptic or quasi-hyperelliptic fibrations","authors":"","doi":"10.1142/9789811215216_0009","DOIUrl":"https://doi.org/10.1142/9789811215216_0009","url":null,"abstract":"","PeriodicalId":249858,"journal":{"name":"Algebraic Surfaces in Positive Characteristics","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131398178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Divisor class groups","authors":"P. L. Clark","doi":"10.1142/9789811215216_0006","DOIUrl":"https://doi.org/10.1142/9789811215216_0006","url":null,"abstract":"We have already defined the Picard group of an arbitrary domain R. The definition we gave was invertible fractional ideals modulo principal fractional ideals. We also noted in passing that a nonzero R-submodule M of K is a fractional ideal exactly when it is locally free of rank 1, and if I and J are fractional ideals, IJ ∼=R I ⊗R J . In other words, the Picard group can equally well be interpreted as the group of isomorphism classes of rank 1 locally free modules.","PeriodicalId":249858,"journal":{"name":"Algebraic Surfaces in Positive Characteristics","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122444189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}