双周期第一莫拉瓦迭加理论的代数迭加理论

IF 1.2 2区数学 Q1 MATHEMATICS Transactions of the American Mathematical Society Pub Date : 2024-03-29 DOI:10.1090/tran/9178

Haldun Özgür Bayındır

{"title":"双周期第一莫拉瓦迭加理论的代数迭加理论","authors":"Haldun Özgür Bayındır","doi":"10.1090/tran/9178","DOIUrl":null,"url":null,"abstract":"<p>Using the root adjunction formalism developed in an earlier work and logarithmic THH, we obtain a simplified computation of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper T left-parenthesis 2 right-parenthesis Subscript asterisk Baseline normal upper K left-parenthesis k u right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>T</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mn>2</mml:mn> <mml:msub> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>∗</mml:mo> </mml:msub> <mml:mrow> <mml:mi mathvariant=\"normal\">K</mml:mi> </mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>k</mml:mi> <mml:mi>u</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">T(2)_*\\mathrm {K}(ku)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p greater-than 3\"> <mml:semantics> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>></mml:mo> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">p>3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Through this, we also produce a new algebraic <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K\"> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding=\"application/x-tex\">K</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-theory computation; namely we obtain <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper T left-parenthesis 2 right-parenthesis Subscript asterisk Baseline normal upper K left-parenthesis k u slash p right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>T</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mn>2</mml:mn> <mml:msub> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>∗</mml:mo> </mml:msub> <mml:mrow> <mml:mi mathvariant=\"normal\">K</mml:mi> </mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>k</mml:mi> <mml:mi>u</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>p</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">T(2)_*\\mathrm {K}(ku/p)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k u slash p\"> <mml:semantics> <mml:mrow> <mml:mi>k</mml:mi> <mml:mi>u</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">ku/p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"2\"> <mml:semantics> <mml:mn>2</mml:mn> <mml:annotation encoding=\"application/x-tex\">2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-periodic Morava <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K\"> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding=\"application/x-tex\">K</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-theory spectrum of height <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"1\"> <mml:semantics> <mml:mn>1</mml:mn> <mml:annotation encoding=\"application/x-tex\">1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Algebraic 𝐾-theory of the two-periodic first Morava 𝐾-theory\",\"authors\":\"Haldun Özgür Bayındır\",\"doi\":\"10.1090/tran/9178\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Using the root adjunction formalism developed in an earlier work and logarithmic THH, we obtain a simplified computation of <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper T left-parenthesis 2 right-parenthesis Subscript asterisk Baseline normal upper K left-parenthesis k u right-parenthesis\\\"> <mml:semantics> <mml:mrow> <mml:mi>T</mml:mi> <mml:mo stretchy=\\\"false\\\">(</mml:mo> <mml:mn>2</mml:mn> <mml:msub> <mml:mo stretchy=\\\"false\\\">)</mml:mo> <mml:mo>∗</mml:mo> </mml:msub> <mml:mrow> <mml:mi mathvariant=\\\"normal\\\">K</mml:mi> </mml:mrow> <mml:mo stretchy=\\\"false\\\">(</mml:mo> <mml:mi>k</mml:mi> <mml:mi>u</mml:mi> <mml:mo stretchy=\\\"false\\\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\\\"application/x-tex\\\">T(2)_*\\\\mathrm {K}(ku)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"p greater-than 3\\\"> <mml:semantics> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>></mml:mo> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding=\\\"application/x-tex\\\">p>3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Through this, we also produce a new algebraic <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper K\\\"> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding=\\\"application/x-tex\\\">K</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-theory computation; namely we obtain <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper T left-parenthesis 2 right-parenthesis Subscript asterisk Baseline normal upper K left-parenthesis k u slash p right-parenthesis\\\"> <mml:semantics> <mml:mrow> <mml:mi>T</mml:mi> <mml:mo stretchy=\\\"false\\\">(</mml:mo> <mml:mn>2</mml:mn> <mml:msub> <mml:mo stretchy=\\\"false\\\">)</mml:mo> <mml:mo>∗</mml:mo> </mml:msub> <mml:mrow> <mml:mi mathvariant=\\\"normal\\\">K</mml:mi> </mml:mrow> <mml:mo stretchy=\\\"false\\\">(</mml:mo> <mml:mi>k</mml:mi> <mml:mi>u</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>p</mml:mi> <mml:mo stretchy=\\\"false\\\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\\\"application/x-tex\\\">T(2)_*\\\\mathrm {K}(ku/p)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"k u slash p\\\"> <mml:semantics> <mml:mrow> <mml:mi>k</mml:mi> <mml:mi>u</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> <mml:annotation encoding=\\\"application/x-tex\\\">ku/p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"2\\\"> <mml:semantics> <mml:mn>2</mml:mn> <mml:annotation encoding=\\\"application/x-tex\\\">2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-periodic Morava <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper K\\\"> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding=\\\"application/x-tex\\\">K</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-theory spectrum of height <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"1\\\"> <mml:semantics> <mml:mn>1</mml:mn> <mml:annotation encoding=\\\"application/x-tex\\\">1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.</p>\",\"PeriodicalId\":23209,\"journal\":{\"name\":\"Transactions of the American Mathematical Society\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-03-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions of the American Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/tran/9178\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of the American Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/tran/9178","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

利用早先研究中发展的根隶属形式和对数 THH，我们得到了 p > 3 p>3 时 T ( 2 ) ∗ K ( k u ) T(2)_*\mathrm {K}(ku) 的简化计算。由此，我们还得到了一个新的代数 K K 理论计算；即我们得到了 T ( 2 ) ∗ K ( k u / p ) T(2)_*\mathrm {K}(ku/p) ，其中 k u / p ku/p 是高度为 1 1 的 2 2 -periodic Morava K K 理论谱。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Algebraic 𝐾-theory of the two-periodic first Morava 𝐾-theory

Using the root adjunction formalism developed in an earlier work and logarithmic THH, we obtain a simplified computation of T ( 2 ) ∗ K ( k u ) T(2)_*\mathrm {K}(ku) for p > 3 p>3 . Through this, we also produce a new algebraic K K -theory computation; namely we obtain T ( 2 ) ∗ K ( k u / p ) T(2)_*\mathrm {K}(ku/p) , where k u / p ku/p is the 2 2 -periodic Morava K K -theory spectrum of height 1 1 .

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

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.

期刊最新文献

A compact extension of Journé’s 𝑇1 theorem on product spaces Solving the Kerzman’s problem on the sup-norm estimate for \overline{∂} on product domains Soap bubbles and convex cones: optimal quantitative rigidity Endomorphisms of mapping tori Commensurated hyperbolic subgroups