{"title":"椭圆曲线的色Selmer群与算术不变量","authors":"Florian Ito Sprung","doi":"10.5802/jtnb.1190","DOIUrl":null,"url":null,"abstract":"Chromatic Selmer groups are modified Selmer groups with local information for supersingular primes p. We sketch their role in establishing the p-primary part of the Birch–Swinnerton-Dyer formula in Sections 2–5, and then study the growth of the Mordell–Weil rank along the Zp-extension of a quadratic imaginary number field in which p splits in Section 6.","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2022-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Chromatic Selmer groups and arithmetic invariants of elliptic curves\",\"authors\":\"Florian Ito Sprung\",\"doi\":\"10.5802/jtnb.1190\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Chromatic Selmer groups are modified Selmer groups with local information for supersingular primes p. We sketch their role in establishing the p-primary part of the Birch–Swinnerton-Dyer formula in Sections 2–5, and then study the growth of the Mordell–Weil rank along the Zp-extension of a quadratic imaginary number field in which p splits in Section 6.\",\"PeriodicalId\":48896,\"journal\":{\"name\":\"Journal De Theorie Des Nombres De Bordeaux\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2022-01-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal De Theorie Des Nombres De Bordeaux\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.5802/jtnb.1190\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal De Theorie Des Nombres De Bordeaux","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.5802/jtnb.1190","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Chromatic Selmer groups and arithmetic invariants of elliptic curves
Chromatic Selmer groups are modified Selmer groups with local information for supersingular primes p. We sketch their role in establishing the p-primary part of the Birch–Swinnerton-Dyer formula in Sections 2–5, and then study the growth of the Mordell–Weil rank along the Zp-extension of a quadratic imaginary number field in which p splits in Section 6.
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