{"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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"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\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"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\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/JAG/709\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/JAG/709","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","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.
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