{"title":"等变连接𝐾-theory","authors":"N. Karpenko, A. Merkurjev","doi":"10.1090/jag/773","DOIUrl":null,"url":null,"abstract":"For separated schemes of finite type over a field with an action of an affine group scheme of finite type, we construct the bi-graded equivariant connective \n\n \n K\n K\n \n\n-theory mapping to the equivariant \n\n \n K\n K\n \n\n-homology of Guillot and the equivariant algebraic \n\n \n K\n K\n \n\n-theory of Thomason. It has all the standard basic properties as the homotopy invariance and localization. We also get the equivariant version of the Brown-Gersten-Quillen spectral sequence and study its convergence.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2021-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Equivariant connective 𝐾-theory\",\"authors\":\"N. Karpenko, A. Merkurjev\",\"doi\":\"10.1090/jag/773\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For separated schemes of finite type over a field with an action of an affine group scheme of finite type, we construct the bi-graded equivariant connective \\n\\n \\n K\\n K\\n \\n\\n-theory mapping to the equivariant \\n\\n \\n K\\n K\\n \\n\\n-homology of Guillot and the equivariant algebraic \\n\\n \\n K\\n K\\n \\n\\n-theory of Thomason. It has all the standard basic properties as the homotopy invariance and localization. We also get the equivariant version of the Brown-Gersten-Quillen spectral sequence and study its convergence.\",\"PeriodicalId\":54887,\"journal\":{\"name\":\"Journal of Algebraic Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2021-10-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebraic Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/jag/773\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebraic Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/jag/773","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
For separated schemes of finite type over a field with an action of an affine group scheme of finite type, we construct the bi-graded equivariant connective
K
K
-theory mapping to the equivariant
K
K
-homology of Guillot and the equivariant algebraic
K
K
-theory of Thomason. It has all the standard basic properties as the homotopy invariance and localization. We also get the equivariant version of the Brown-Gersten-Quillen spectral sequence and study its convergence.
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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