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Massey products and elliptic curves 梅西产品和椭圆曲线
IF 1.8 1区 数学
Proceedings of the London Mathematical Society Pub Date : 2022-05-27 DOI: 10.1112/plms.12541
F. Bleher, T. Chinburg, J. Gillibert
{"title":"Massey products and elliptic curves","authors":"F. Bleher, T. Chinburg, J. Gillibert","doi":"10.1112/plms.12541","DOIUrl":"https://doi.org/10.1112/plms.12541","url":null,"abstract":"We study the vanishing of Massey products of order at least 3 for absolutely irreducible smooth projective curves over a field with coefficients in Z/ℓ$mathbb {Z}/ell$ . We mainly focus on elliptic curves, for which we obtain a complete characterization of when triple Massey products do not vanish.","PeriodicalId":49667,"journal":{"name":"Proceedings of the London Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42657452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Poincaré constant on manifolds with ends 端点流形上的庞卡罗常数
IF 1.8 1区 数学
Proceedings of the London Mathematical Society Pub Date : 2022-05-12 DOI: 10.1112/plms.12522
A. Grigor’yan, Satoshi Ishiwata, L. Saloff‐Coste
{"title":"Poincaré constant on manifolds with ends","authors":"A. Grigor’yan, Satoshi Ishiwata, L. Saloff‐Coste","doi":"10.1112/plms.12522","DOIUrl":"https://doi.org/10.1112/plms.12522","url":null,"abstract":"We obtain optimal estimates of the Poincaré constant of central balls on manifolds with finitely many ends. Surprisingly enough, the Poincaré constant is determined by the second largest end. The proof is based on the argument by Kusuoka–Stroock where the heat kernel estimates on the central balls play an essential role. For this purpose, we extend earlier heat kernel estimates obtained by the authors to a larger class of parabolic manifolds with ends.","PeriodicalId":49667,"journal":{"name":"Proceedings of the London Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47216874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Classifying the expanding attractors on the figure‐eight knot exterior and the non‐transitive Anosov flows on the Franks–Williams manifold 分类了8字形结外部的膨胀吸引子和Franks-Williams流形上的非传递Anosov流
IF 1.8 1区 数学
Proceedings of the London Mathematical Society Pub Date : 2022-04-26 DOI: 10.1112/plms.12444
Jiagang Yang, B. Yu
{"title":"Classifying the expanding attractors on the figure‐eight knot exterior and the non‐transitive Anosov flows on the Franks–Williams manifold","authors":"Jiagang Yang, B. Yu","doi":"10.1112/plms.12444","DOIUrl":"https://doi.org/10.1112/plms.12444","url":null,"abstract":"The figure‐eight knot exterior N0$N_0$ supports a natural DA (derived from Anosov) expanding attractor, with which Franks–Williams constructed the first example of non‐transitive Anosov flow. This flow lies in a 3‐manifold M0$M_0$ which is the double of N0$N_0$ . We call M0$M_0$ by the Franks–Williams manifold. In this paper, we prove that, up to orbit‐equivalence, this DA expanding attractor is the unique expanding attractor supported by N0$N_0$ . We also show that, up to orbit‐equivalence, the non‐transitive Anosov flow constructed by Franks and Williams is the unique non‐transitive Anosov flow supported by M0$M_0$ . We also extend these results to a more general context.","PeriodicalId":49667,"journal":{"name":"Proceedings of the London Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45363936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
W$W$ ‐algebras associated to surfaces 与曲面相关的W$W$-代数
IF 1.8 1区 数学
Proceedings of the London Mathematical Society Pub Date : 2022-04-14 DOI: 10.1112/plms.12435
Andrei Neguț
{"title":"W$W$ ‐algebras associated to surfaces","authors":"Andrei Neguț","doi":"10.1112/plms.12435","DOIUrl":"https://doi.org/10.1112/plms.12435","url":null,"abstract":"We define an integral form of the deformed W$W$ ‐algebra of type glr${mathfrak {gl}}_r$ , and construct its action on the K$K$ ‐theory groups of moduli spaces of rank r$r$ stable sheaves on a smooth projective surface S$S$ , under certain assumptions. Our construction generalizes the action studied by Nakajima, Grojnowski and Baranovsky in cohomology, although the appearance of deformed W$W$ ‐algebras by generators and relations is a new feature. Physically, this action encodes the Alday–Gaiotto–Tachikawa correspondence for 5‐dimensional supersymmetric gauge theory on S×$S times$ circle.","PeriodicalId":49667,"journal":{"name":"Proceedings of the London Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47091211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 5
Issue Information 问题信息
IF 1.8 1区 数学
Proceedings of the London Mathematical Society Pub Date : 2022-04-01 DOI: 10.1112/plms.12410
{"title":"Issue Information","authors":"","doi":"10.1112/plms.12410","DOIUrl":"https://doi.org/10.1112/plms.12410","url":null,"abstract":"","PeriodicalId":49667,"journal":{"name":"Proceedings of the London Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48667468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
The density of polynomials of degree n$n$ over Zp${mathbb {Z}}_p$ having exactly r$r$ roots in Qp${mathbb {Q}}_p$ 次多项式n$n$ / Zp${mathbb {Z}}_p$在Qp${mathbb {Q}}_p$中恰好有r$r$根的密度
IF 1.8 1区 数学
Proceedings of the London Mathematical Society Pub Date : 2022-03-17 DOI: 10.1112/plms.12438
M. Bhargava, J. Cremona, T. Fisher, Stevan Gajović
{"title":"The density of polynomials of degree n$n$ over Zp${mathbb {Z}}_p$ having exactly r$r$ roots in Qp${mathbb {Q}}_p$","authors":"M. Bhargava, J. Cremona, T. Fisher, Stevan Gajović","doi":"10.1112/plms.12438","DOIUrl":"https://doi.org/10.1112/plms.12438","url":null,"abstract":"We determine the probability that a random polynomial of degree n$n$ over Zp${mathbb {Z}}_p$ has exactly r$r$ roots in Qp${mathbb {Q}}_p$ , and show that it is given by a rational function of p$p$ that is invariant under replacing p$p$ by 1/p$1/p$ .","PeriodicalId":49667,"journal":{"name":"Proceedings of the London Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44819731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
The finite jet determination problem for CR maps of positive codimension into Nash manifolds 纳什流形中正余维CR映射的有限射流确定问题
IF 1.8 1区 数学
Proceedings of the London Mathematical Society Pub Date : 2022-03-14 DOI: 10.1112/plms.12439
B. Lamel, N. Mir
{"title":"The finite jet determination problem for CR maps of positive codimension into Nash manifolds","authors":"B. Lamel, N. Mir","doi":"10.1112/plms.12439","DOIUrl":"https://doi.org/10.1112/plms.12439","url":null,"abstract":"We prove the first general finite jet determination result in positive codimension for CR maps from real‐analytic minimal submanifolds M⊂CN$Msubset mathbb {C}^N$ into Nash (real) submanifolds M′⊂CN′$M^{prime }subset mathbb {C}^{N^{prime }}$ . For a sheaf S$mathcal {S}$ of C∞$mathcal {C}^infty$ ‐smooth CR maps from M$M$ into M′$M^{prime }$ , we show that the non‐existence of so‐called 2‐approximate CR S$mathcal {S}$‐deformations from M$M$ into M′$M^{prime }$ implies the following strong finite jet determination property: There exists a map ℓ:M→Z+$ell colon Mrightarrow {mathbb {Z}}_+$ , bounded on compact subsets of M$M$ , such that for every point p∈M$pin M$ , whenever f,g$f,g$ are two elements of Sp$mathcal {S}_p$ with jpℓ(p)f=jpℓ(p)g$j^{ell (p)}_pf=j^{ell (p)}_pg$ , then f=g$f=g$ . Applying the deformation point of view allows a unified treatment of a number of classes of target manifolds, which includes, among others, strictly pseudoconvex, Levi–non‐degenerate, but also some particularly important Levi‐degenerate targets, such as boundaries of classical domains.","PeriodicalId":49667,"journal":{"name":"Proceedings of the London Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44832784","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 4
Regularity of viscosity solutions of the σk$sigma _k$ ‐Loewner–Nirenberg problem σk$σ_k$-Loewner–Nirenberg问题粘度解的正则性
IF 1.8 1区 数学
Proceedings of the London Mathematical Society Pub Date : 2022-03-10 DOI: 10.1112/plms.12536
Yanyan Li, Luc Nguyen, Jingang Xiong
{"title":"Regularity of viscosity solutions of the σk$sigma _k$ ‐Loewner–Nirenberg problem","authors":"Yanyan Li, Luc Nguyen, Jingang Xiong","doi":"10.1112/plms.12536","DOIUrl":"https://doi.org/10.1112/plms.12536","url":null,"abstract":"We study the regularity of the viscosity solution u$u$ of the σk$sigma _k$ ‐Loewner–Nirenberg problem on a bounded smooth domain Ω⊂Rn$Omega subset mathbb {R}^n$ for k⩾2$k geqslant 2$ . It was known that u$u$ is locally Lipschitz in Ω$Omega$ . We prove that, with d$d$ being the distance function to ∂Ω$partial Omega$ and δ>0$delta > 0$ sufficiently small, u$u$ is smooth in {0","PeriodicalId":49667,"journal":{"name":"Proceedings of the London Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42365487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
The intersection spectrum of 3‐chromatic intersecting hypergraphs 三色相交超图的相交谱
IF 1.8 1区 数学
Proceedings of the London Mathematical Society Pub Date : 2022-03-10 DOI: 10.1112/plms.12436
Matija Bucić, Stefan Glock, B. Sudakov
{"title":"The intersection spectrum of 3‐chromatic intersecting hypergraphs","authors":"Matija Bucić, Stefan Glock, B. Sudakov","doi":"10.1112/plms.12436","DOIUrl":"https://doi.org/10.1112/plms.12436","url":null,"abstract":"For a hypergraph H$H$ , define its intersection spectrum I(H)$I(H)$ as the set of all intersection sizes |E∩F|$|Ecap F|$ of distinct edges E,F∈E(H)$E,Fin E(H)$ . In their seminal paper from 1973 which introduced the local lemma, Erdős and Lovász asked: how large must the intersection spectrum of a k$k$ ‐uniform 3‐chromatic intersecting hypergraph be? They showed that such a hypergraph must have at least three intersection sizes, and conjectured that the size of the intersection spectrum tends to infinity with k$k$ . Despite the problem being reiterated several times over the years by Erdős and other researchers, the lower bound of three intersection sizes has remarkably withstood any improvement until now. In this paper, we prove the Erdős–Lovász conjecture in a strong form by showing that there are at least k1/2−o(1)$k^{1/2-o(1)}$ intersection sizes. Our proof consists of a delicate interplay between Ramsey‐type arguments and a density increment approach.","PeriodicalId":49667,"journal":{"name":"Proceedings of the London Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46901137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Determination of a class of permutation quadrinomials 一类置换四项的确定
IF 1.8 1区 数学
Proceedings of the London Mathematical Society Pub Date : 2022-03-08 DOI: 10.1112/plms.12540
Zhiguo Ding, Michael E. Zieve
{"title":"Determination of a class of permutation quadrinomials","authors":"Zhiguo Ding, Michael E. Zieve","doi":"10.1112/plms.12540","DOIUrl":"https://doi.org/10.1112/plms.12540","url":null,"abstract":"We determine all permutation polynomials over Fq2$mathbb {F}_{q^2}$ of the form XrA(Xq−1)$X^r A(X^{q-1})$ where, for some Q$Q$ that is a power of the characteristic of Fq$mathbb {F}_q$ , we have r≡Q+1(modq+1)$requiv Q+1pmod {q+1}$ and all terms of A(X)$A(X)$ have degrees in {0,1,Q,Q+1}$lbrace 0,1,Q,Q+1rbrace$ . We use this classification to resolve eight conjectures and open problems from the literature, and we list 77 recent results from the literature that follow immediately from the simplest special cases of our result. Our proof makes a novel use of geometric techniques in a situation where they previously did not seem applicable, namely to understand the arithmetic of high‐degree rational functions over small finite fields, despite the fact that in this situation the Weil bounds do not provide useful information.","PeriodicalId":49667,"journal":{"name":"Proceedings of the London Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49088026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 4
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