{"title":"论经典亚当斯谱序列中积的非琐碎性","authors":"Linan Zhong, Hao Zhao","doi":"10.37256/cm.4420232994","DOIUrl":null,"url":null,"abstract":"Let p ≥ 11 be an odd prime and q = 2(p − 1). Suppose that n ≥ 1 with n ≠ 5. Let 0 ≤ s < p − 4 and t = s + 2 + t = s + 2 + (s + 2)p + (s + 3)p2 + (s +4)p3 + pn . This paper shows that the product element δs+4h0bn−1 ∈ ExtAs+7,tq+s (Z/p,Z/p) is a nontrivial permanent cycle in the classical Adams spectral sequence, where δs+4 denotes the 4th Greek letter element.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"47 4","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Nontriviality of a Product in the Classical Adams Spectral Sequence\",\"authors\":\"Linan Zhong, Hao Zhao\",\"doi\":\"10.37256/cm.4420232994\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let p ≥ 11 be an odd prime and q = 2(p − 1). Suppose that n ≥ 1 with n ≠ 5. Let 0 ≤ s < p − 4 and t = s + 2 + t = s + 2 + (s + 2)p + (s + 3)p2 + (s +4)p3 + pn . This paper shows that the product element δs+4h0bn−1 ∈ ExtAs+7,tq+s (Z/p,Z/p) is a nontrivial permanent cycle in the classical Adams spectral sequence, where δs+4 denotes the 4th Greek letter element.\",\"PeriodicalId\":29767,\"journal\":{\"name\":\"Contemporary Mathematics\",\"volume\":\"47 4\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-11-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Contemporary Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37256/cm.4420232994\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Contemporary Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37256/cm.4420232994","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
设 p ≥ 11 为奇数素数，q = 2(p - 1)。假设 n ≥ 1，n≠5。设 0≤s < p - 4，且 t = s + 2 + t = s + 2 + (s + 2)p + (s + 3)p2 + (s + 4)p3 + pn。本文证明了乘积元素 δs+4h0bn-1∈ ExtAs+7,tq+s (Z/p,Z/p) 是经典亚当斯谱序列中的一个非小永久循环，其中 δs+4 表示第 4 个希腊字母元素。
On Nontriviality of a Product in the Classical Adams Spectral Sequence
Let p ≥ 11 be an odd prime and q = 2(p − 1). Suppose that n ≥ 1 with n ≠ 5. Let 0 ≤ s < p − 4 and t = s + 2 + t = s + 2 + (s + 2)p + (s + 3)p2 + (s +4)p3 + pn . This paper shows that the product element δs+4h0bn−1 ∈ ExtAs+7,tq+s (Z/p,Z/p) is a nontrivial permanent cycle in the classical Adams spectral sequence, where δs+4 denotes the 4th Greek letter element.
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