{"title":"Bivariant derived algebraic cobordism","authors":"Toni Annala","doi":"10.1090/jag/754","DOIUrl":null,"url":null,"abstract":"We extend the derived algebraic bordism of Lowrey and Schürg to a bivariant theory in the sense of Fulton and MacPherson and establish some of its basic properties. As a special case, we obtain a completely new theory of cobordism rings of singular quasi-projective schemes. The extended cobordism is shown to specialize to algebraic \n\n \n \n K\n 0\n \n K^0\n \n\n analogously to the Conner-Floyd theorem in topology. We also give a candidate for the correct definition of Chow rings of singular schemes.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2018-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"18","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebraic Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/jag/754","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 18
Abstract
We extend the derived algebraic bordism of Lowrey and Schürg to a bivariant theory in the sense of Fulton and MacPherson and establish some of its basic properties. As a special case, we obtain a completely new theory of cobordism rings of singular quasi-projective schemes. The extended cobordism is shown to specialize to algebraic
K
0
K^0
analogously to the Conner-Floyd theorem in topology. We also give a candidate for the correct definition of Chow rings of singular schemes.
期刊介绍：
The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology.
This journal, published quarterly with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.
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