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Galois codescent for motivic tame kernels 动机驯服核的伽罗瓦代码
IF 0.4
Annales Mathematiques du Quebec Pub Date : 2025-01-27 DOI: 10.1007/s40316-024-00233-8
J. Assim, A. Movahhedi
{"title":"Galois codescent for motivic tame kernels","authors":"J. Assim,&nbsp;A. Movahhedi","doi":"10.1007/s40316-024-00233-8","DOIUrl":"10.1007/s40316-024-00233-8","url":null,"abstract":"<div><p>Let <i>L</i>/<i>F</i> be a finite Galois extension of number fields with an arbitrary Galois group <i>G</i>. We give an explicit description of the kernel of the natural map on motivic cohomology of the rings of integers <span>(H^2_mathcal {M}(o_L, {textbf{Z}}(i))_{G} {longrightarrow } H^2_mathcal {M}(o_F, {textbf{Z}}(i)))</span>. Using the link between motivic cohomology and <i>K</i>-theory, we deduce genus formulae for all even <i>K</i>-groups <span>(K_{2i-2}(o_F))</span> of the ring of integers. As a by-product, we answer a question raised by B. Kahn about a signature map.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 2","pages":"503 - 555"},"PeriodicalIF":0.4,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223724","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
Radial limits of solutions to elliptic partial differential equations 椭圆型偏微分方程解的径向极限
IF 0.4
Annales Mathematiques du Quebec Pub Date : 2025-01-20 DOI: 10.1007/s40316-025-00241-2
Paul M. Gauthier, Mohammad Shirazi
{"title":"Radial limits of solutions to elliptic partial differential equations","authors":"Paul M. Gauthier,&nbsp;Mohammad Shirazi","doi":"10.1007/s40316-025-00241-2","DOIUrl":"10.1007/s40316-025-00241-2","url":null,"abstract":"<div><p>For certain elliptic differential operators <i>L</i>,  we study the behaviour of solutions to <span>(Lu=0,)</span> as we tend to the boundary along radii in strictly starlike domains in <span>(mathbb {R}^n, nge 3.)</span> Analogous results are obtained in other special domains. Our approach involves introducing harmonic line bundles as instances of Brelot harmonic spaces and approximating continuous functions by harmonic functions on appropriate subsets. We are required to approximate on certain closed sets, which is not obvious, since the space of continuous functions on an (unbounded) closed set, endowed with the topology of uniform convergence, is not a topological vector space, though it is both a vector space and a topological space.\u0000</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 2","pages":"375 - 402"},"PeriodicalIF":0.4,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223714","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 (Lambda )-submodules with finite index of the plus/minus Selmer group over anticyclotomic ({{,mathrm{mathbb {Z}},}}_{p})-extension at inert primes 抗细胞分裂上正/负Selmer群有限指数的(Lambda ) -子模({{,mathrm{mathbb {Z}},}}_{p}) -在惰性素数上的扩展
IF 0.4
Annales Mathematiques du Quebec Pub Date : 2025-01-11 DOI: 10.1007/s40316-024-00236-5
Ryota Shii
{"title":"On (Lambda )-submodules with finite index of the plus/minus Selmer group over anticyclotomic ({{,mathrm{mathbb {Z}},}}_{p})-extension at inert primes","authors":"Ryota Shii","doi":"10.1007/s40316-024-00236-5","DOIUrl":"10.1007/s40316-024-00236-5","url":null,"abstract":"<div><p>Let <i>K</i> be an imaginary quadratic field where a prime number <span>(p ge 5)</span> is inert. Let <i>E</i> be an elliptic curve defined over <i>K</i> and suppose that <i>E</i> has good supersingular reduction at <i>p</i>. In this paper, we prove that the plus/minus Selmer group of <i>E</i> over the anticyclotomic <span>({{,mathrm{mathbb {Z}},}}_{p})</span>-extension of <i>K</i> has no proper <span>(Lambda )</span>-submodules of finite index under mild assumptions for <i>E</i>. This is an analogous result to R. Greenberg and B. D. Kim for the anticyclotomic <span>({{,mathrm{mathbb {Z}},}}_{p})</span>-extension essentially. By applying the results of A. Agboola–B. Howard or A. Burungale–K. Büyükboduk–A. Lei, we can also construct examples satisfying the assumptions of our theorem.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 2","pages":"477 - 490"},"PeriodicalIF":0.4,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223715","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
Uniqueness of Lagrangians in (T^*{mathbb {R}}P^2) 拉格朗日量的唯一性 (T^*{mathbb {R}}P^2)
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2025-01-11 DOI: 10.1007/s40316-024-00238-3
Nikolas Adaloglou
{"title":"Uniqueness of Lagrangians in (T^*{mathbb {R}}P^2)","authors":"Nikolas Adaloglou","doi":"10.1007/s40316-024-00238-3","DOIUrl":"10.1007/s40316-024-00238-3","url":null,"abstract":"<div><p>We present a new and simpler proof of the fact that any Lagrangian <span>({mathbb {R}}P^2)</span> in <span>(T^*{mathbb {R}}P^2)</span> is Hamiltonian isotopic to the zero section. Our proof mirrors the one given by Li and Wu for the Hamiltonian uniqueness of Lagrangians in <span>(T^*S^2)</span>, using surgery to turn Lagrangian spheres into symplectic ones. The main novel contribution is a detailed proof of the folklore fact that the complement of a symplectic quadric in <span>({mathbb {C}}P^2)</span> can be identified with the unit cotangent disc bundle of <span>({mathbb {R}}P^2)</span>.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 1","pages":"215 - 222"},"PeriodicalIF":0.5,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143848947","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
Closed flat Riemannian 4-manifolds 闭合平坦黎曼4流形
IF 0.4
Annales Mathematiques du Quebec Pub Date : 2025-01-10 DOI: 10.1007/s40316-024-00231-w
Thomas P. Lambert, John G. Ratcliffe, Steven T. Tschantz
{"title":"Closed flat Riemannian 4-manifolds","authors":"Thomas P. Lambert,&nbsp;John G. Ratcliffe,&nbsp;Steven T. Tschantz","doi":"10.1007/s40316-024-00231-w","DOIUrl":"10.1007/s40316-024-00231-w","url":null,"abstract":"<div><p>In this paper, we describe the classification of all the geometric fibrations of a closed flat Riemannian 4-manifold over a connected 1-orbifold.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 2","pages":"287 - 333"},"PeriodicalIF":0.4,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40316-024-00231-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223718","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
Some remarks on critical sets of Laplace eigenfunctions 关于拉普拉斯特征函数临界集的若干注记
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2025-01-09 DOI: 10.1007/s40316-024-00240-9
Chris Judge, Sugata Mondal
{"title":"Some remarks on critical sets of Laplace eigenfunctions","authors":"Chris Judge,&nbsp;Sugata Mondal","doi":"10.1007/s40316-024-00240-9","DOIUrl":"10.1007/s40316-024-00240-9","url":null,"abstract":"<p>We study the set of critical points of a solution to <span>(Delta u = lambda cdot u)</span> and in particular components of the critical set that have codimension 1. We show, for example, that if a second Neumann eigenfunction of a simply connected polygon <i>P</i> has infinitely many critical points, then <i>P</i> is a rectangle.</p>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"49 1","pages":"155 - 163"},"PeriodicalIF":0.5,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143848944","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
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
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