{"title":"论 p$-adic 几何中向量束的某些扩展","authors":"Serin Hong","doi":"10.4310/mrl.2023.v30.n5.a6","DOIUrl":null,"url":null,"abstract":"Given two arbitrary vector bundles on the Fargues–Fontaine curve, we give an explicit criterion in terms of Harder–Narasimhan polygons on whether they realize a semistable vector bundle as their extensions. Our argument is largely combinatorial and builds upon the dimension analysis of certain moduli spaces of bundle maps developed in $\\href{https://doi.org/10.1017/S1474748020000183}{[1]}$.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"28 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On certain extensions of vector bundles in $p$-adic geometry\",\"authors\":\"Serin Hong\",\"doi\":\"10.4310/mrl.2023.v30.n5.a6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Given two arbitrary vector bundles on the Fargues–Fontaine curve, we give an explicit criterion in terms of Harder–Narasimhan polygons on whether they realize a semistable vector bundle as their extensions. Our argument is largely combinatorial and builds upon the dimension analysis of certain moduli spaces of bundle maps developed in $\\\\href{https://doi.org/10.1017/S1474748020000183}{[1]}$.\",\"PeriodicalId\":49857,\"journal\":{\"name\":\"Mathematical Research Letters\",\"volume\":\"28 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-05-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Research Letters\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/mrl.2023.v30.n5.a6\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Research Letters","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/mrl.2023.v30.n5.a6","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
On certain extensions of vector bundles in $p$-adic geometry
Given two arbitrary vector bundles on the Fargues–Fontaine curve, we give an explicit criterion in terms of Harder–Narasimhan polygons on whether they realize a semistable vector bundle as their extensions. Our argument is largely combinatorial and builds upon the dimension analysis of certain moduli spaces of bundle maps developed in $\href{https://doi.org/10.1017/S1474748020000183}{[1]}$.
期刊介绍:
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