{"title":"Deligne-Mumford堆栈的Atiya-Segal定理及其应用","authors":"A. Krishna, Bhamidi Sreedhar","doi":"10.1090/jag/755","DOIUrl":null,"url":null,"abstract":"We prove an Atiyah-Segal isomorphism for the higher \n\n \n K\n K\n \n\n-theory of coherent sheaves on quotient Deligne-Mumford stacks over \n\n \n \n C\n \n \\mathbb {C}\n \n\n. As an application, we prove the Grothendieck-Riemann-Roch theorem for such stacks. This theorem establishes an isomorphism between the higher \n\n \n K\n K\n \n\n-theory of coherent sheaves on a Deligne-Mumford stack and the higher Chow groups of its inertia stack. Furthermore, this isomorphism is covariant for proper maps between Deligne-Mumford stacks.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2017-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/jag/755","citationCount":"4","resultStr":"{\"title\":\"Atiyah-Segal theorem for Deligne-Mumford stacks and applications\",\"authors\":\"A. Krishna, Bhamidi Sreedhar\",\"doi\":\"10.1090/jag/755\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove an Atiyah-Segal isomorphism for the higher \\n\\n \\n K\\n K\\n \\n\\n-theory of coherent sheaves on quotient Deligne-Mumford stacks over \\n\\n \\n \\n C\\n \\n \\\\mathbb {C}\\n \\n\\n. As an application, we prove the Grothendieck-Riemann-Roch theorem for such stacks. This theorem establishes an isomorphism between the higher \\n\\n \\n K\\n K\\n \\n\\n-theory of coherent sheaves on a Deligne-Mumford stack and the higher Chow groups of its inertia stack. Furthermore, this isomorphism is covariant for proper maps between Deligne-Mumford stacks.\",\"PeriodicalId\":54887,\"journal\":{\"name\":\"Journal of Algebraic Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2017-01-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1090/jag/755\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebraic Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/jag/755\",\"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/755","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Atiyah-Segal theorem for Deligne-Mumford stacks and applications
We prove an Atiyah-Segal isomorphism for the higher
K
K
-theory of coherent sheaves on quotient Deligne-Mumford stacks over
C
\mathbb {C}
. As an application, we prove the Grothendieck-Riemann-Roch theorem for such stacks. This theorem establishes an isomorphism between the higher
K
K
-theory of coherent sheaves on a Deligne-Mumford stack and the higher Chow groups of its inertia stack. Furthermore, this isomorphism is covariant for proper maps between Deligne-Mumford stacks.
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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