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Annales Mathematiques du Quebec最新文献

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Generators for the moduli space of parabolic bundle 抛物束模空间的生成器
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2024-12-30 DOI: 10.1007/s40316-024-00232-9
Lisa Jeffrey, Yukai Zhang
{"title":"Generators for the moduli space of parabolic bundle","authors":"Lisa Jeffrey,&nbsp;Yukai Zhang","doi":"10.1007/s40316-024-00232-9","DOIUrl":"10.1007/s40316-024-00232-9","url":null,"abstract":"<div><p>The purpose of this note is to find explicit representatives in de Rham cohomology for the generators of the cohomology of the moduli space of parabolic bundles, analogous to the results of [5] for the moduli space of vector bundles. Further we use the explicit generators to compute the intersection pairing of its cohomology.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 1","pages":"223 - 236"},"PeriodicalIF":0.5,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143848948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The heat kernel on curvilinear polygonal domains in surfaces 曲面上曲线多边形区域上的热核
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2024-12-27 DOI: 10.1007/s40316-024-00237-4
Medet Nursultanov, Julie Rowlett, David Sher
{"title":"The heat kernel on curvilinear polygonal domains in surfaces","authors":"Medet Nursultanov,&nbsp;Julie Rowlett,&nbsp;David Sher","doi":"10.1007/s40316-024-00237-4","DOIUrl":"10.1007/s40316-024-00237-4","url":null,"abstract":"<p>We construct the heat kernel on curvilinear polygonal domains in arbitrary surfaces for Dirichlet, Neumann, and Robin boundary conditions as well as mixed problems, including those of Zaremba type. We compute the short time asymptotic expansion of the heat trace and apply this expansion to demonstrate a collection of results showing that corners are spectral invariants.</p>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 1","pages":"1 - 61"},"PeriodicalIF":0.5,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40316-024-00237-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143848952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the (mathbb {Z}_2)-valued index of elliptic odd symmetric operators on non-compact manifolds 非紧流形上椭圆奇对称算子的(mathbb {Z}_2)值索引
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2024-12-26 DOI: 10.1007/s40316-024-00228-5
Maxim Braverman, Ahmad Reza Haj Saeedi Sadegh
{"title":"On the (mathbb {Z}_2)-valued index of elliptic odd symmetric operators on non-compact manifolds","authors":"Maxim Braverman,&nbsp;Ahmad Reza Haj Saeedi Sadegh","doi":"10.1007/s40316-024-00228-5","DOIUrl":"10.1007/s40316-024-00228-5","url":null,"abstract":"<div><p>We investigate elliptic operators with a symmetry that forces their index to vanish. We study the secondary index, defined modulo 2. We examine Callias-type operators with this symmetry on non-compact manifolds and establish mod 2 versions of the Gromov–Lawson relative index theorem, the Callias index theorem, and the Boutet de Monvel’s index theorem for Toeplitz operators.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 1","pages":"73 - 103"},"PeriodicalIF":0.5,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143848942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On fine Mordell–Weil groups over (mathbb {Z}_{p})-extensions of an imaginary quadratic field 虚二次域(mathbb {Z}_{p})上的精细modell - weil群
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2024-12-24 DOI: 10.1007/s40316-024-00230-x
Meng Fai Lim
{"title":"On fine Mordell–Weil groups over (mathbb {Z}_{p})-extensions of an imaginary quadratic field","authors":"Meng Fai Lim","doi":"10.1007/s40316-024-00230-x","DOIUrl":"10.1007/s40316-024-00230-x","url":null,"abstract":"<div><p>Let <i>E</i> be an elliptic curve over <span>(mathbb {Q})</span>. Greenberg has posed a question whether the structure of the fine Selmer group over the cyclotomic <span>(mathbb {Z}_{p})</span>-extension of <span>(mathbb {Q})</span> can be described by cyclotomic polynomials in a certain precise manner. A recent work of Lei has made progress on this problem by proving that the fine Mordell–Weil group (in the sense of Wuthrich) does have this required property. The goal of this paper is to study analogous questions of Greenberg over various <span>(mathbb {Z}_{p})</span>-extensions of an imaginary quadratic field <i>F</i>. In particular, when the elliptic curve has complex multiplication by the ring of integers of the imaginary quadratic field, we obtain results that are analogous to those of Lei over the cyclotomic <span>(mathbb {Z}_{p})</span>-extension and anti-cyclotomic <span>(mathbb {Z}_{p})</span>-extension of <i>F</i>. In the event that the elliptic curve has good ordinary reduction at the prime <i>p</i>, we further obtain a result over the <span>(mathbb {Z}_{p})</span>-extension of <i>F</i> unramified outside precisely one of the prime of <i>F</i> above <i>p</i>. Finally, we study the situation of an elliptic curve over the anticyclotomic <span>(mathbb {Z}_{p})</span>-extension under the generalized Heegner hypothesis. Along the way, we establish an analogous result for the BDP-Selmer group. This latter result is then applied to obtain a relation between the BDP <i>p</i>-adic <i>L</i>-function and the Mordell–Weil rank growth in the anticyclotomic <span>(mathbb {Z}_{p})</span>-extension which may be of independent interest.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 1","pages":"253 - 278"},"PeriodicalIF":0.5,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143848950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A note on the capacities of Lagrangian p-sum 关于拉格朗日p和的容量的注记
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2024-12-23 DOI: 10.1007/s40316-024-00235-6
Filip Broćić
{"title":"A note on the capacities of Lagrangian p-sum","authors":"Filip Broćić","doi":"10.1007/s40316-024-00235-6","DOIUrl":"10.1007/s40316-024-00235-6","url":null,"abstract":"<div><p>In this short note, we construct an explicit embedding of the rescaling of the <i>p</i>-sum <span>(Koplus _p K^{circ })</span> of the centrally symmetric convex domain <i>K</i> and it’s polar <span>(K^{circ })</span> to the product <span>(K times K^{circ })</span>. The rescaling constant is sharp in some cases. Additionally, we comment about the strong Viterbo conjecture for <span>(Koplus _p K^{circ })</span>.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 1","pages":"279 - 286"},"PeriodicalIF":0.5,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143848951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Nodal sets of Laplacian eigenfunctions with an eigenvalue of multiplicity 2 特征值多重性为2的拉普拉斯特征函数的节点集
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2024-12-19 DOI: 10.1007/s40316-024-00227-6
Andrew Lyons
{"title":"Nodal sets of Laplacian eigenfunctions with an eigenvalue of multiplicity 2","authors":"Andrew Lyons","doi":"10.1007/s40316-024-00227-6","DOIUrl":"10.1007/s40316-024-00227-6","url":null,"abstract":"<div><p>We study the effects of a domain deformation to the nodal set of Laplacian eigenfunctions when the eigenvalue is degenerate. In particular, we study deformations of a rectangle that perturb one side and how they change the nodal sets corresponding to an eigenvalue of multiplicity 2. We establish geometric properties, such as number of nodal domains, presence of crossings, and boundary intersections, of nodal sets for a large class of boundary deformations and study how these properties change along each eigenvalue branch for small perturbations. We show that internal crossings of the nodal set break under generic deformations and obtain estimates on the location and regularity of the nodal sets on the perturbed rectangle.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 1","pages":"105 - 153"},"PeriodicalIF":0.5,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143848943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Circular orderability and quandles 循环有序性和阶乘
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2024-12-19 DOI: 10.1007/s40316-024-00234-7
Idrissa Ba, Mohamed Elhamdadi
{"title":"Circular orderability and quandles","authors":"Idrissa Ba,&nbsp;Mohamed Elhamdadi","doi":"10.1007/s40316-024-00234-7","DOIUrl":"10.1007/s40316-024-00234-7","url":null,"abstract":"<p>In this paper, we introduce the notion of circular orderability for quandles. We show that the set of all right (respectively left) circular orderings of a quandle is a compact topological space. We also show that the space of right (respectively left) orderings of a quandle embeds in its space of right (respectively left) circular orderings. Examples of quandles that are not left circularly orderable and examples of quandles that are neither left nor right circularly orderable are given.</p>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 1","pages":"63 - 72"},"PeriodicalIF":0.5,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143848997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sur les modules d’Iwasawa S-ramifiés T-décomposés 岩泽S-分支T-分解模块
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2024-04-10 DOI: 10.1007/s40316-024-00223-w
Jean-François Jaulent
{"title":"Sur les modules d’Iwasawa S-ramifiés T-décomposés","authors":"Jean-François Jaulent","doi":"10.1007/s40316-024-00223-w","DOIUrl":"10.1007/s40316-024-00223-w","url":null,"abstract":"<p>We correct the faulty formulas given in a previous article and we compute the defect group for the Iwasawa <span>(lambda )</span> invariants attached to the <i>S</i>-ramified <i>T</i>-decomposed abelian pro-<span>(ell )</span>-extensions over the <span>({{mathbb {Z}}_ell })</span>-cyclotomic extension of a number field. As a consequence, we extend the results of Itoh, Mizusawa and Ozaki on tamely ramified Iwasawa modules for the cyclotomic <span>({{mathbb {Z}}_ell })</span>-extension of abelian fields.</p>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 1","pages":"237 - 252"},"PeriodicalIF":0.5,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143848949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Estimates for low Steklov eigenvalues of surfaces with several boundary components 具有多个边界分量的曲面的低Steklov特征值估计
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2024-03-26 DOI: 10.1007/s40316-024-00221-y
Hélène Perrin
{"title":"Estimates for low Steklov eigenvalues of surfaces with several boundary components","authors":"Hélène Perrin","doi":"10.1007/s40316-024-00221-y","DOIUrl":"10.1007/s40316-024-00221-y","url":null,"abstract":"<p>In this article, we give computable lower bounds for the first non-zero Steklov eigenvalue <span>(sigma _1)</span> of a compact connected 2-dimensional Riemannian manifold <i>M</i> with several cylindrical boundary components. These estimates show how the geometry of <i>M</i> away from the boundary affects this eigenvalue. They involve geometric quantities specific to manifolds with boundary such as the extrinsic diameter of the boundary. In a second part, we give lower and upper estimates for the low Steklov eigenvalues of a hyperbolic surface with a geodesic boundary in terms of the length of some families of geodesics. This result is similar to a well known result of Schoen, Wolpert and Yau for Laplace eigenvalues on a closed hyperbolic surface.</p>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 1","pages":"165 - 184"},"PeriodicalIF":0.5,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40316-024-00221-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143848945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Thin Monodromy in (textrm{O}(5)) Thin Monodromy in （textrm{O}(5))
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2024-03-25 DOI: 10.1007/s40316-024-00222-x
Jitendra Bajpai, Martin Nitsche
{"title":"Thin Monodromy in (textrm{O}(5))","authors":"Jitendra Bajpai,&nbsp;Martin Nitsche","doi":"10.1007/s40316-024-00222-x","DOIUrl":"10.1007/s40316-024-00222-x","url":null,"abstract":"<p>This article studies the orthogonal hypergeometric groups of degree five. We establish the thinness of 12 out of the 19 hypergeometric groups of type <i>O</i>(3, 2) from [4, Table 6]. Some of these examples are associated with Calabi-Yau 4-folds. We also establish the thinness of 9 out of the 17 hypergeometric groups of type <i>O</i>(4, 1) from [13], where the thinness of 7 other cases was already proven. The <i>O</i>(4, 1) type groups were predicted to be all thin and our result leaves just one case open.</p>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"48 2","pages":"349 - 360"},"PeriodicalIF":0.5,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40316-024-00222-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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