{"title":"双元几何中的准 F 分裂 II","authors":"Tatsuro Kawakami, Teppei Takamatsu, Hiromu Tanaka, Jakub Witaszek, Fuetaro Yobuko, Shou Yoshikawa","doi":"10.1112/plms.12593","DOIUrl":null,"url":null,"abstract":"Over an algebraically closed field of characteristic <span data-altimg=\"/cms/asset/a0d7faab-7168-4a9c-b74e-972a24c48863/plms12593-math-0001.png\"></span><math altimg=\"urn:x-wiley:00246115:media:plms12593:plms12593-math-0001\" display=\"inline\" location=\"graphic/plms12593-math-0001.png\">\n<semantics>\n<mrow>\n<mi>p</mi>\n<mo>></mo>\n<mn>41</mn>\n</mrow>\n$p&gt;41$</annotation>\n</semantics></math>, we prove that three-dimensional <span data-altimg=\"/cms/asset/cf78c1f3-24c3-4fec-9668-03f7c418e99c/plms12593-math-0002.png\"></span><math altimg=\"urn:x-wiley:00246115:media:plms12593:plms12593-math-0002\" display=\"inline\" location=\"graphic/plms12593-math-0002.png\">\n<semantics>\n<mi mathvariant=\"double-struck\">Q</mi>\n$\\mathbb {Q}$</annotation>\n</semantics></math>-factorial affine klt varieties are quasi-<span data-altimg=\"/cms/asset/7b306e81-fd40-4a25-ba07-064f6dd57036/plms12593-math-0003.png\"></span><math altimg=\"urn:x-wiley:00246115:media:plms12593:plms12593-math-0003\" display=\"inline\" location=\"graphic/plms12593-math-0003.png\">\n<semantics>\n<mi>F</mi>\n$F$</annotation>\n</semantics></math>-split. Furthermore, we show that the bound on the characteristic is optimal.","PeriodicalId":49667,"journal":{"name":"Proceedings of the London Mathematical Society","volume":"25 1","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quasi-F-splittings in birational geometry II\",\"authors\":\"Tatsuro Kawakami, Teppei Takamatsu, Hiromu Tanaka, Jakub Witaszek, Fuetaro Yobuko, Shou Yoshikawa\",\"doi\":\"10.1112/plms.12593\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Over an algebraically closed field of characteristic <span data-altimg=\\\"/cms/asset/a0d7faab-7168-4a9c-b74e-972a24c48863/plms12593-math-0001.png\\\"></span><math altimg=\\\"urn:x-wiley:00246115:media:plms12593:plms12593-math-0001\\\" display=\\\"inline\\\" location=\\\"graphic/plms12593-math-0001.png\\\">\\n<semantics>\\n<mrow>\\n<mi>p</mi>\\n<mo>></mo>\\n<mn>41</mn>\\n</mrow>\\n$p&gt;41$</annotation>\\n</semantics></math>, we prove that three-dimensional <span data-altimg=\\\"/cms/asset/cf78c1f3-24c3-4fec-9668-03f7c418e99c/plms12593-math-0002.png\\\"></span><math altimg=\\\"urn:x-wiley:00246115:media:plms12593:plms12593-math-0002\\\" display=\\\"inline\\\" location=\\\"graphic/plms12593-math-0002.png\\\">\\n<semantics>\\n<mi mathvariant=\\\"double-struck\\\">Q</mi>\\n$\\\\mathbb {Q}$</annotation>\\n</semantics></math>-factorial affine klt varieties are quasi-<span data-altimg=\\\"/cms/asset/7b306e81-fd40-4a25-ba07-064f6dd57036/plms12593-math-0003.png\\\"></span><math altimg=\\\"urn:x-wiley:00246115:media:plms12593:plms12593-math-0003\\\" display=\\\"inline\\\" location=\\\"graphic/plms12593-math-0003.png\\\">\\n<semantics>\\n<mi>F</mi>\\n$F$</annotation>\\n</semantics></math>-split. Furthermore, we show that the bound on the characteristic is optimal.\",\"PeriodicalId\":49667,\"journal\":{\"name\":\"Proceedings of the London Mathematical Society\",\"volume\":\"25 1\",\"pages\":\"\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2024-04-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the London Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1112/plms.12593\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the London Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1112/plms.12593","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Over an algebraically closed field of characteristic , we prove that three-dimensional -factorial affine klt varieties are quasi--split. Furthermore, we show that the bound on the characteristic is optimal.
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