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Level compatibility in Sharifi’s conjecture Sharifi猜想中的层次兼容性
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-08-14 DOI: 10.4153/s0008439523000267
E. Lecouturier, Jun Wang
{"title":"Level compatibility in Sharifi’s conjecture","authors":"E. Lecouturier, Jun Wang","doi":"10.4153/s0008439523000267","DOIUrl":"https://doi.org/10.4153/s0008439523000267","url":null,"abstract":"Sharifi has constructed a map from the first homology of the modular curve $X_1(M)$ to the $K$-group $K_2(mathbf{Z}[zeta_M, frac{1}{M}])$, where $zeta_M$ is a primitive $M$th root of unity. We study how these maps relate when $M$ varies. Our method relies on the techniques developed by Sharifi and Venkatesh.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48184100","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
Determining sets for holomorphic functions on the symmetrized bidisk 对称双盘上全纯函数的确定集
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-08-12 DOI: 10.4153/S0008439523000103
Bata Krishna Das, Poornendu Kumar, H. Sau
{"title":"Determining sets for holomorphic functions on the symmetrized bidisk","authors":"Bata Krishna Das, Poornendu Kumar, H. Sau","doi":"10.4153/S0008439523000103","DOIUrl":"https://doi.org/10.4153/S0008439523000103","url":null,"abstract":"Abstract A subset \u0000${mathcal D}$\u0000 of a domain \u0000$Omega subset {mathbb C}^d$\u0000 is determining for an analytic function \u0000$f:Omega to overline {{mathbb D}}$\u0000 if whenever an analytic function \u0000$g:Omega rightarrow overline {{mathbb D}}$\u0000 coincides with f on \u0000${mathcal D}$\u0000 , equals to f on whole \u0000$Omega $\u0000 . This note finds several sufficient conditions for a subset of the symmetrized bidisk to be determining. For any \u0000$Ngeq 1$\u0000 , a set consisting of \u0000$N^2-N+1$\u0000 many points is constructed which is determining for any rational inner function with a degree constraint. We also investigate when the intersection of the symmetrized bidisk intersected with some special algebraic varieties can be determining for rational inner functions.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48628260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The complexity of higher Chow groups 高等周氏群的复杂性
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-07-29 DOI: 10.4153/S0008439522000509
Genival da Silva, James D. Lewis
{"title":"The complexity of higher Chow groups","authors":"Genival da Silva, James D. Lewis","doi":"10.4153/S0008439522000509","DOIUrl":"https://doi.org/10.4153/S0008439522000509","url":null,"abstract":"Abstract Let \u0000$X/{mathbb C}$\u0000 be a smooth projective variety. We consider two integral invariants, one of which is the level of the Hodge cohomology algebra \u0000$H^*(X,{mathbb C})$\u0000 and the other involving the complexity of the higher Chow groups \u0000${mathrm {CH}}^*(X,m;{mathbb Q})$\u0000 for \u0000$mgeq 0$\u0000 . We conjecture that these two invariants are the same and accordingly provide some strong evidence in support of this.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48046316","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
From the Ideal Theorem to the class number 从理想定理到类数
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-07-24 DOI: 10.4153/s0008439523000425
O. Bordellès
{"title":"From the Ideal Theorem to the class number","authors":"O. Bordellès","doi":"10.4153/s0008439523000425","DOIUrl":"https://doi.org/10.4153/s0008439523000425","url":null,"abstract":"In this note, we provide an explicit upper bound for $h_K mathcal{R}_K d_K^{-1/2}$ which depends on an effective constant in the error term of the Ideal Theorem.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44082621","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
Zero and uniqueness sets for Fock spaces Fock空间的零集和唯一集
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-07-21 DOI: 10.4153/S0008439522000492
D. Aadi, Y. Omari
{"title":"Zero and uniqueness sets for Fock spaces","authors":"D. Aadi, Y. Omari","doi":"10.4153/S0008439522000492","DOIUrl":"https://doi.org/10.4153/S0008439522000492","url":null,"abstract":"Abstract We characterize zero sets for which every subset remains a zero set too in the Fock space \u0000$mathcal {F}^p$\u0000 , \u0000$1leq p<infty $\u0000 . We are also interested in the study of a stability problem for some examples of uniqueness set with zero excess in Fock spaces.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49358167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On Hardy kernels as reproducing kernels 论哈代核作为再生核
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-06-17 DOI: 10.4153/S0008439522000406
J. Oliva-Maza
{"title":"On Hardy kernels as reproducing kernels","authors":"J. Oliva-Maza","doi":"10.4153/S0008439522000406","DOIUrl":"https://doi.org/10.4153/S0008439522000406","url":null,"abstract":"Abstract Hardy kernels are a useful tool to define integral operators on Hilbertian spaces like \u0000$L^2(mathbb R^+)$\u0000 or \u0000$H^2(mathbb C^+)$\u0000 . These kernels entail an algebraic \u0000$L^1$\u0000 -structure which is used in this work to study the range spaces of those operators as reproducing kernel Hilbert spaces. We obtain their reproducing kernels, which in the \u0000$L^2(mathbb R^+)$\u0000 case turn out to be Hardy kernels as well. In the \u0000$H^2(mathbb C^+)$\u0000 scenario, the reproducing kernels are given by holomorphic extensions of Hardy kernels. Other results presented here are theorems of Paley–Wiener type, and a connection with one-sided Hilbert transforms.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45337449","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
Groups whose Chermak–Delgado lattice is a subgroup lattice of an abelian group Chermak–Delgado格是阿贝尔群的子群格的群
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-06-17 DOI: 10.4153/S0008439522000418
Lijian An
{"title":"Groups whose Chermak–Delgado lattice is a subgroup lattice of an abelian group","authors":"Lijian An","doi":"10.4153/S0008439522000418","DOIUrl":"https://doi.org/10.4153/S0008439522000418","url":null,"abstract":"Abstract The Chermak–Delgado lattice of a finite group G is a self-dual sublattice of the subgroup lattice of G. In this paper, we prove that, for any finite abelian group A, there exists a finite group G such that the Chermak–Delgado lattice of G is a subgroup lattice of A.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49098697","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
Optimization of the anisotropic Cheeger constant with respect to the anisotropy 各向异性Cheeger常数的各向异性优化
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-06-15 DOI: 10.4153/S0008439523000152
E. Parini, Giorgio Saracco
{"title":"Optimization of the anisotropic Cheeger constant with respect to the anisotropy","authors":"E. Parini, Giorgio Saracco","doi":"10.4153/S0008439523000152","DOIUrl":"https://doi.org/10.4153/S0008439523000152","url":null,"abstract":"Abstract Given an open, bounded set \u0000$Omega $\u0000 in \u0000$mathbb {R}^N$\u0000 , we consider the minimization of the anisotropic Cheeger constant \u0000$h_K(Omega )$\u0000 with respect to the anisotropy K, under a volume constraint on the associated unit ball. In the planar case, under the assumption that K is a convex, centrally symmetric body, we prove the existence of a minimizer. Moreover, if \u0000$Omega $\u0000 is a ball, we show that the optimal anisotropy K is not a ball and that, among all regular polygons, the square provides the minimal value.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46083684","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
A result on the c2 invariant for powers of primes 关于素数幂的c2不变量的一个结果
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-06-14 DOI: 10.4153/s0008439523000243
Maria S. Esipova, K. Yeats
{"title":"A result on the c2 invariant for powers of primes","authors":"Maria S. Esipova, K. Yeats","doi":"10.4153/s0008439523000243","DOIUrl":"https://doi.org/10.4153/s0008439523000243","url":null,"abstract":"The $c_2$ invariant is an arithmetic graph invariant related to quantum field theory. We give a relation modulo $p$ between the $c_2$ invariant at $p$ and the $c_2$ invariant at $p^s$ by proving a relation modulo $p$ between certain coefficients of powers of products of particularly nice polynomials. The relation at the level of the $c_2$ invariant provides evidence for a conjecture of Schnetz.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47433116","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
Vertices of the Harder and Narasimhan polygons and the laws of large numbers Harder和Narasimhan多边形的顶点与大数定律
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-06-14 DOI: 10.4153/S000843952200039X
Nathan Grieve
{"title":"Vertices of the Harder and Narasimhan polygons and the laws of large numbers","authors":"Nathan Grieve","doi":"10.4153/S000843952200039X","DOIUrl":"https://doi.org/10.4153/S000843952200039X","url":null,"abstract":"Abstract We build on the recent techniques of Codogni and Patakfalvi (2021, Inventiones Mathematicae 223, 811–894), which were used to establish theorems about semi-positivity of the Chow Mumford line bundles for families of \u0000$mathrm {K}$\u0000 -semistable Fano varieties. Here, we apply the Central Limit Theorem to ascertain the asymptotic probabilistic nature of the vertices of the Harder and Narasimhan polygons. As an application of our main result, we use it to establish a filtered vector space analogue of the main technical result of Codogni and Patakfalvi (2021, Inventiones Mathematicae 223, 811–894). In doing so, we expand upon the slope stability theory, for filtered vector spaces, that was initiated by Faltings and Wüstholz (1994, Inventiones Mathematicae 116, 109–138). One source of inspiration for our abstract study of Harder and Narasimhan data, which is a concept that we define here, is the lattice reduction methods of Grayson (1984, Commentarii Mathematici Helvetic 59, 600–634). Another is the work of Faltings and Wüstholz (1994, Inventiones Mathematicae 116, 109–138), and Evertse and Ferretti (2013, Annals of Mathematics 177, 513–590), which is within the context of Diophantine approximation for projective varieties.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45132044","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
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