{"title":"刚性解析空间上的\\ widdeparen{}-模II: Kashiwara的等价性","authors":"K. Ardakov, S. Wadsley","doi":"10.1090/JAG/709","DOIUrl":null,"url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\">\n <mml:semantics>\n <mml:mi>X</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">X</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> be a smooth rigid analytic space. We prove that the category of co-admissible <inline-formula content-type=\"math/tex\">\n<tex-math>\n\\wideparen {\\mathcal {D}_X}</tex-math></inline-formula>-modules supported on a closed smooth subvariety <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper Y\">\n <mml:semantics>\n <mml:mi>Y</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">Y</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> of <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\">\n <mml:semantics>\n <mml:mi>X</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">X</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> is naturally equivalent to the category of co-admissible <inline-formula content-type=\"math/tex\">\n<tex-math>\n\\wideparen {\\mathcal {D}_Y}</tex-math></inline-formula>-modules and use this result to construct a large family of pairwise non-isomorphic simple co-admissible <inline-formula content-type=\"math/tex\">\n<tex-math>\n\\wideparen {\\mathcal {D}_X}</tex-math></inline-formula>-modules.</p>","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2018-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/JAG/709","citationCount":"4","resultStr":"{\"title\":\"\\\\wideparen{𝒟}-modules on rigid analytic spaces II: Kashiwara’s equivalence\",\"authors\":\"K. Ardakov, S. Wadsley\",\"doi\":\"10.1090/JAG/709\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Let <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper X\\\">\\n <mml:semantics>\\n <mml:mi>X</mml:mi>\\n <mml:annotation encoding=\\\"application/x-tex\\\">X</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula> be a smooth rigid analytic space. We prove that the category of co-admissible <inline-formula content-type=\\\"math/tex\\\">\\n<tex-math>\\n\\\\wideparen {\\\\mathcal {D}_X}</tex-math></inline-formula>-modules supported on a closed smooth subvariety <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper Y\\\">\\n <mml:semantics>\\n <mml:mi>Y</mml:mi>\\n <mml:annotation encoding=\\\"application/x-tex\\\">Y</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula> of <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper X\\\">\\n <mml:semantics>\\n <mml:mi>X</mml:mi>\\n <mml:annotation encoding=\\\"application/x-tex\\\">X</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula> is naturally equivalent to the category of co-admissible <inline-formula content-type=\\\"math/tex\\\">\\n<tex-math>\\n\\\\wideparen {\\\\mathcal {D}_Y}</tex-math></inline-formula>-modules and use this result to construct a large family of pairwise non-isomorphic simple co-admissible <inline-formula content-type=\\\"math/tex\\\">\\n<tex-math>\\n\\\\wideparen {\\\\mathcal {D}_X}</tex-math></inline-formula>-modules.</p>\",\"PeriodicalId\":54887,\"journal\":{\"name\":\"Journal of Algebraic Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2018-07-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1090/JAG/709\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebraic Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/JAG/709\",\"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/709","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
\wideparen{𝒟}-modules on rigid analytic spaces II: Kashiwara’s equivalence
Let XX be a smooth rigid analytic space. We prove that the category of co-admissible
\wideparen {\mathcal {D}_X}-modules supported on a closed smooth subvariety YY of XX is naturally equivalent to the category of co-admissible
\wideparen {\mathcal {D}_Y}-modules and use this result to construct a large family of pairwise non-isomorphic simple co-admissible
\wideparen {\mathcal {D}_X}-modules.
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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