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RANK JUMPS AND GROWTH OF SHAFAREVICH–TATE GROUPS FOR ELLIPTIC CURVES IN -EXTENSIONS 椭圆曲线在-扩展中的shafarevic - tate群的秩跳和增长
IF 0.7 4区 数学
Journal of the Australian Mathematical Society Pub Date : 2023-05-29 DOI: 10.1017/s1446788723000034
Lea Beneish, Debanjana Kundu, Anwesh Ray
{"title":"RANK JUMPS AND GROWTH OF SHAFAREVICH–TATE GROUPS FOR ELLIPTIC CURVES IN -EXTENSIONS","authors":"Lea Beneish, Debanjana Kundu, Anwesh Ray","doi":"10.1017/s1446788723000034","DOIUrl":"https://doi.org/10.1017/s1446788723000034","url":null,"abstract":"\u0000 Let p be a prime. In this paper, we use techniques from Iwasawa theory to study questions about rank jump of elliptic curves in cyclic extensions of degree p. We also study growth of the p-primary Selmer group and the Shafarevich–Tate group in cyclic degree-p extensions and improve upon previously known results in this direction.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73538715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
JAZ volume 114 issue 3 Cover and Front matter jazz第114卷第3期封面和封面问题
IF 0.7 4区 数学
Journal of the Australian Mathematical Society Pub Date : 2023-05-12 DOI: 10.1017/s1446788722000271
{"title":"JAZ volume 114 issue 3 Cover and Front matter","authors":"","doi":"10.1017/s1446788722000271","DOIUrl":"https://doi.org/10.1017/s1446788722000271","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81187626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
JAZ volume 114 issue 3 Cover and Back matter jazz第114卷第3期封面和封底
IF 0.7 4区 数学
Journal of the Australian Mathematical Society Pub Date : 2023-05-12 DOI: 10.1017/s1446788722000283
{"title":"JAZ volume 114 issue 3 Cover and Back matter","authors":"","doi":"10.1017/s1446788722000283","DOIUrl":"https://doi.org/10.1017/s1446788722000283","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83672973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
INDEX 指数
IF 0.7 4区 数学
Journal of the Australian Mathematical Society Pub Date : 2023-05-01 DOI: 10.1016/s1878-6480(23)00206-9
{"title":"INDEX","authors":"","doi":"10.1016/s1878-6480(23)00206-9","DOIUrl":"https://doi.org/10.1016/s1878-6480(23)00206-9","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88200640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
NONREALIZABILITY OF CERTAIN REPRESENTATIONS IN FUSION SYSTEMS 融合系统中某些表征的不可实现性
4区 数学
Journal of the Australian Mathematical Society Pub Date : 2023-04-11 DOI: 10.1017/s1446788723000022
Bob Oliver
{"title":"NONREALIZABILITY OF CERTAIN REPRESENTATIONS IN FUSION SYSTEMS","authors":"Bob Oliver","doi":"10.1017/s1446788723000022","DOIUrl":"https://doi.org/10.1017/s1446788723000022","url":null,"abstract":"Abstract For a finite abelian p -group A and a subgroup $Gamma le operatorname {mathrm {Aut}}(A)$ , we say that the pair $(Gamma ,A)$ is fusion realizable if there is a saturated fusion system ${mathcal {F}}$ over a finite p -group $Sge A$ such that $C_S(A)=A$ , $operatorname {mathrm {Aut}}_{{mathcal {F}}}(A)=Gamma $ as subgroups of $operatorname {mathrm {Aut}}(A)$ , and . In this paper, we develop tools to show that certain representations are not fusion realizable in this sense. For example, we show, for $p=2$ or $3$ and $Gamma $ one of the Mathieu groups, that the only ${mathbb {F}}_pGamma $ -modules that are fusion realizable (up to extensions by trivial modules) are the Todd modules and in some cases their duals.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134955096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
JAZ volume 114 issue 2 Cover and Back matter jazz第114卷第2期封面和封底
IF 0.7 4区 数学
Journal of the Australian Mathematical Society Pub Date : 2023-03-06 DOI: 10.1017/s144678872200026x
{"title":"JAZ volume 114 issue 2 Cover and Back matter","authors":"","doi":"10.1017/s144678872200026x","DOIUrl":"https://doi.org/10.1017/s144678872200026x","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83406120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
JAZ volume 114 issue 2 Cover and Front matter jazz 114卷第2期封面和封面问题
IF 0.7 4区 数学
Journal of the Australian Mathematical Society Pub Date : 2023-03-06 DOI: 10.1017/s1446788722000258
{"title":"JAZ volume 114 issue 2 Cover and Front matter","authors":"","doi":"10.1017/s1446788722000258","DOIUrl":"https://doi.org/10.1017/s1446788722000258","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74892298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
ON THE NUMBER OF QUADRATIC ORTHOMORPHISMS THAT PRODUCE MAXIMALLY NONASSOCIATIVE QUASIGROUPS 关于产生最大非结合拟群的二次正态的个数
4区 数学
Journal of the Australian Mathematical Society Pub Date : 2023-02-20 DOI: 10.1017/s1446788722000386
Aleš Drápal, Ian M. Wanless
{"title":"ON THE NUMBER OF QUADRATIC ORTHOMORPHISMS THAT PRODUCE MAXIMALLY NONASSOCIATIVE QUASIGROUPS","authors":"Aleš Drápal, Ian M. Wanless","doi":"10.1017/s1446788722000386","DOIUrl":"https://doi.org/10.1017/s1446788722000386","url":null,"abstract":"Abstract Let q be an odd prime power and suppose that $a,bin mathbb {F}_q$ are such that $ab$ and $(1{-}a)(1{-}b)$ are nonzero squares. Let $Q_{a,b} = (mathbb {F}_q,*)$ be the quasigroup in which the operation is defined by $u*v=u+a(v{-}u)$ if $v-u$ is a square, and $u*v=u+b(v{-}u)$ if $v-u$ is a nonsquare. This quasigroup is called maximally nonassociative if it satisfies $x*(y*z) = (x*y)*z Leftrightarrow x=y=z$ . Denote by $sigma (q)$ the number of $(a,b)$ for which $Q_{a,b}$ is maximally nonassociative. We show that there exist constants $alpha approx 0.029,08$ and $beta approx 0.012,59$ such that if $qequiv 1 bmod 4$ , then $lim sigma (q)/q^2 = alpha $ , and if $q equiv 3 bmod 4$ , then $lim sigma (q)/q^2 = beta $ .","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135081074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
JAZ volume 114 issue 1 Cover and Front matter jazz 114卷第1期封面和封面问题
IF 0.7 4区 数学
Journal of the Australian Mathematical Society Pub Date : 2023-01-13 DOI: 10.1017/s1446788722000234
{"title":"JAZ volume 114 issue 1 Cover and Front matter","authors":"","doi":"10.1017/s1446788722000234","DOIUrl":"https://doi.org/10.1017/s1446788722000234","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77056398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
JAZ volume 114 issue 1 Cover and Back matter jazz第114卷第1期封面和封底
IF 0.7 4区 数学
Journal of the Australian Mathematical Society Pub Date : 2023-01-13 DOI: 10.1017/s1446788722000246
{"title":"JAZ volume 114 issue 1 Cover and Back matter","authors":"","doi":"10.1017/s1446788722000246","DOIUrl":"https://doi.org/10.1017/s1446788722000246","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88798013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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