亚当斯式地图在构图下是不稳定的

Proceedings of the American Mathematical Society, Series B Pub Date : 2022-02-28 DOI:10.1090/bproc/137

Robert Burklund, Ishan Levy, Piotr Pstrkagowski

{"title":"亚当斯式地图在构图下是不稳定的","authors":"Robert Burklund, Ishan Levy, Piotr Pstrkagowski","doi":"10.1090/bproc/137","DOIUrl":null,"url":null,"abstract":"<p>We give a simple counterexample to the plausible conjecture that Adams-type maps of ring spectra are stable under composition. We then show that over a field, this failure is quite extreme, as any map to an <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper E Subscript normal infinity\">\n <mml:semantics>\n <mml:msub>\n <mml:mrow class=\"MJX-TeXAtom-ORD\">\n <mml:mi mathvariant=\"double-struck\">E</mml:mi>\n </mml:mrow>\n <mml:mrow class=\"MJX-TeXAtom-ORD\">\n <mml:mi mathvariant=\"normal\">∞</mml:mi>\n </mml:mrow>\n </mml:msub>\n <mml:annotation encoding=\"application/x-tex\">\\mathbb {E}_{\\infty }</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>-<inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k\">\n <mml:semantics>\n <mml:mi>k</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">k</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>-algebra is a transfinite composition of Adams-type maps.</p>","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"85 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Adams-type maps are not stable under composition\",\"authors\":\"Robert Burklund, Ishan Levy, Piotr Pstrkagowski\",\"doi\":\"10.1090/bproc/137\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We give a simple counterexample to the plausible conjecture that Adams-type maps of ring spectra are stable under composition. We then show that over a field, this failure is quite extreme, as any map to an <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"double-struck upper E Subscript normal infinity\\\">\\n <mml:semantics>\\n <mml:msub>\\n <mml:mrow class=\\\"MJX-TeXAtom-ORD\\\">\\n <mml:mi mathvariant=\\\"double-struck\\\">E</mml:mi>\\n </mml:mrow>\\n <mml:mrow class=\\\"MJX-TeXAtom-ORD\\\">\\n <mml:mi mathvariant=\\\"normal\\\">∞</mml:mi>\\n </mml:mrow>\\n </mml:msub>\\n <mml:annotation encoding=\\\"application/x-tex\\\">\\\\mathbb {E}_{\\\\infty }</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula>-<inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"k\\\">\\n <mml:semantics>\\n <mml:mi>k</mml:mi>\\n <mml:annotation encoding=\\\"application/x-tex\\\">k</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula>-algebra is a transfinite composition of Adams-type maps.</p>\",\"PeriodicalId\":106316,\"journal\":{\"name\":\"Proceedings of the American Mathematical Society, Series B\",\"volume\":\"85 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the American Mathematical Society, Series B\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/bproc/137\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the American Mathematical Society, Series B","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/bproc/137","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

我们给出了一个简单的反例来证明环谱的adams型图在组成下是稳定的。然后，我们证明了在一个域上，这种失败是相当极端的，因为任何映射到E∞\mathbb E＿{}{\infty - k k -代数都是adams型映射的超限组合。}

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Adams-type maps are not stable under composition

We give a simple counterexample to the plausible conjecture that Adams-type maps of ring spectra are stable under composition. We then show that over a field, this failure is quite extreme, as any map to an E ∞ \mathbb {E}_{\infty } - k k -algebra is a transfinite composition of Adams-type maps.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Proceedings of the American Mathematical Society, Series B

CiteScore

1.60

自引率

0.00%

发文量