{"title":"的K(1)-局部同伦 \\(\\mathrm {tmf}\\wedge \\mathrm {tmf}\\)","authors":"Dominic Leon Culver, Paul VanKoughnett","doi":"10.1007/s40062-021-00283-7","DOIUrl":null,"url":null,"abstract":"<div><p>As a step towards understanding the <span>\\(\\mathrm {tmf}\\)</span>-based Adams spectral sequence, we compute the <i>K</i>(1)-local homotopy of <span>\\(\\mathrm {tmf}\\wedge \\mathrm {tmf}\\)</span>, using a small presentation of <span>\\(L_{K(1)}\\mathrm {tmf}\\)</span> due to Hopkins. We also describe the <i>K</i>(1)-local <span>\\(\\mathrm {tmf}\\)</span>-based Adams spectral sequence.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-021-00283-7","citationCount":"0","resultStr":"{\"title\":\"On the K(1)-local homotopy of \\\\(\\\\mathrm {tmf}\\\\wedge \\\\mathrm {tmf}\\\\)\",\"authors\":\"Dominic Leon Culver, Paul VanKoughnett\",\"doi\":\"10.1007/s40062-021-00283-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>As a step towards understanding the <span>\\\\(\\\\mathrm {tmf}\\\\)</span>-based Adams spectral sequence, we compute the <i>K</i>(1)-local homotopy of <span>\\\\(\\\\mathrm {tmf}\\\\wedge \\\\mathrm {tmf}\\\\)</span>, using a small presentation of <span>\\\\(L_{K(1)}\\\\mathrm {tmf}\\\\)</span> due to Hopkins. We also describe the <i>K</i>(1)-local <span>\\\\(\\\\mathrm {tmf}\\\\)</span>-based Adams spectral sequence.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2021-07-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1007/s40062-021-00283-7\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40062-021-00283-7\",\"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://link.springer.com/article/10.1007/s40062-021-00283-7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the K(1)-local homotopy of \(\mathrm {tmf}\wedge \mathrm {tmf}\)
As a step towards understanding the \(\mathrm {tmf}\)-based Adams spectral sequence, we compute the K(1)-local homotopy of \(\mathrm {tmf}\wedge \mathrm {tmf}\), using a small presentation of \(L_{K(1)}\mathrm {tmf}\) due to Hopkins. We also describe the K(1)-local \(\mathrm {tmf}\)-based Adams spectral sequence.
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