{"title":"椭圆上同调在同伦以内是唯一的","authors":"J. M. Davies","doi":"10.1017/S1446788722000209","DOIUrl":null,"url":null,"abstract":"Abstract Homotopy theory folklore tells us that the sheaf defining the cohomology theory \n$\\operatorname {\\mathrm {Tmf}}$\n of topological modular forms is unique up to homotopy. Here we provide a proof of this fact, although we claim no originality for the statement. This retroactively reconciles all previous constructions of \n$\\operatorname {\\mathrm {Tmf}}$\n .","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"ELLIPTIC COHOMOLOGY IS UNIQUE UP TO HOMOTOPY\",\"authors\":\"J. M. Davies\",\"doi\":\"10.1017/S1446788722000209\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Homotopy theory folklore tells us that the sheaf defining the cohomology theory \\n$\\\\operatorname {\\\\mathrm {Tmf}}$\\n of topological modular forms is unique up to homotopy. Here we provide a proof of this fact, although we claim no originality for the statement. This retroactively reconciles all previous constructions of \\n$\\\\operatorname {\\\\mathrm {Tmf}}$\\n .\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2021-06-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/S1446788722000209\",\"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/10.1017/S1446788722000209","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Abstract Homotopy theory folklore tells us that the sheaf defining the cohomology theory
$\operatorname {\mathrm {Tmf}}$
of topological modular forms is unique up to homotopy. Here we provide a proof of this fact, although we claim no originality for the statement. This retroactively reconciles all previous constructions of
$\operatorname {\mathrm {Tmf}}$
.
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