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Annales Mathematiques du Quebec最新文献

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Higher codimension Iwasawa theory for elliptic curves with supersingular reduction 超奇异约化椭圆曲线的高协维Iwasawa理论
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2023-05-15 DOI: 10.1007/s40316-023-00216-1
Takenori Kataoka
{"title":"Higher codimension Iwasawa theory for elliptic curves with supersingular reduction","authors":"Takenori Kataoka","doi":"10.1007/s40316-023-00216-1","DOIUrl":"10.1007/s40316-023-00216-1","url":null,"abstract":"<p>Bleher et al. began studying higher codimension Iwasawa theory for classical Iwasawa modules. Subsequently, Lei and Palvannan studied an analogue for elliptic curves with supersingular reduction. In this paper, we obtain a vast generalization of the work of Lei and Palvannan. A key technique is an approach to the work of Bleher et al. that the author previously proposed. For this purpose, we also study the structure of ±-norm subgroups and duality properties of multiply-signed Selmer groups.</p>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"48 2","pages":"379 - 406"},"PeriodicalIF":0.5,"publicationDate":"2023-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47415821","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
Ramification of p-power torsion points of formal groups 形式群的p-幂扭点的分支
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2023-05-11 DOI: 10.1007/s40316-023-00214-3
Adrian Iovita, Jackson S. Morrow, Alexandru Zaharescu
{"title":"Ramification of p-power torsion points of formal groups","authors":"Adrian Iovita,&nbsp;Jackson S. Morrow,&nbsp;Alexandru Zaharescu","doi":"10.1007/s40316-023-00214-3","DOIUrl":"10.1007/s40316-023-00214-3","url":null,"abstract":"<div><p>Let <i>p</i> be a rational prime, let <i>F</i> denote a finite, unramified extension of <span>(mathbb {Q}_p)</span>, let <i>K</i> be the completion of the maximal unramified extension of <span>(mathbb {Q}_p)</span>, and let <span>(overline{K})</span> be some fixed algebraic closure of <i>K</i>. Let <i>A</i> be an abelian variety defined over <i>F</i>, with good reduction, let <span>(mathcal {A})</span> denote the Néron model of <i>A</i> over <span>(textrm{Spec}(mathcal {O}_F))</span>, and let <span>(widehat{mathcal {A}})</span> be the formal completion of <span>(mathcal {A})</span> along the identity of its special fiber, i.e. the formal group of <i>A</i>. In this work, we prove two results concerning the ramification of <i>p</i>-power torsion points on <span>(widehat{mathcal {A}})</span>. One of our main results describes conditions on <span>(widehat{mathcal {A}})</span>, base changed to <span>(text {Spf}(mathcal {O}_K) )</span>, for which the field <span>(K(widehat{mathcal {A}}[p])/K)</span> i s a tamely ramified extension where <span>(widehat{mathcal {A}}[p])</span> denotes the group of <i>p</i>-torsion points of <span>(widehat{mathcal {A}})</span> over <span>(mathcal {O}_{overline{K}})</span>. This result generalizes previous work when <i>A</i> is 1-dimensional and work of Arias-de-Reyna when <i>A</i> is the Jacobian of certain genus 2 hyperelliptic curves.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"48 2","pages":"361 - 378"},"PeriodicalIF":0.5,"publicationDate":"2023-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42565048","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 p-adic interpolation of generalized Heegner cycles and integral Perrin-Riou twist I 广义Heegner环和积分Perrin-Riou扭转的p进插值
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2023-03-02 DOI: 10.1007/s40316-023-00213-4
Shinichi Kobayashi
{"title":"A p-adic interpolation of generalized Heegner cycles and integral Perrin-Riou twist I","authors":"Shinichi Kobayashi","doi":"10.1007/s40316-023-00213-4","DOIUrl":"10.1007/s40316-023-00213-4","url":null,"abstract":"<div><p>In this paper, we develop an integral refinement of the Perrin-Riou theory of exponential maps. We also formulate the Perrin-Riou theory for anticyclotomic deformation of modular forms in terms of the theory of the Serre–Tate local moduli and interpolate generalized Heegner cycles <i>p</i>-adically.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"47 1","pages":"73 - 116"},"PeriodicalIF":0.5,"publicationDate":"2023-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46718623","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: 5
On the classification of (({mathfrak {g}},K))-modules generated by nearly holomorphic Hilbert–Siegel modular forms and projection operators 近全纯Hilbert-Siegel模形式与投影算子生成的$$({mathfrak {g}},K)$$ (g, K) -模的分类
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2023-02-16 DOI: 10.1007/s40316-023-00211-6
Shuji Horinaga
{"title":"On the classification of (({mathfrak {g}},K))-modules generated by nearly holomorphic Hilbert–Siegel modular forms and projection operators","authors":"Shuji Horinaga","doi":"10.1007/s40316-023-00211-6","DOIUrl":"10.1007/s40316-023-00211-6","url":null,"abstract":"<div><p>We classify the <span>(({mathfrak {g}},K))</span>-modules generated by nearly holomorphic Hilbert–Siegel modular forms by the global method. As an application, we study the image of projection operators on the space of nearly holomorphic Hilbert–Siegel modular forms with respect to infinitesimal characters in terms of <span>(({mathfrak {g}},K))</span>-modules.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"48 2","pages":"309 - 348"},"PeriodicalIF":0.5,"publicationDate":"2023-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43198161","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
Constructing Galois representations with large Iwasawa (lambda )-invariant 构造具有大Iwasawa λ不变量的伽罗瓦表示$$lambda $$
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2023-01-28 DOI: 10.1007/s40316-023-00212-5
Anwesh Ray
{"title":"Constructing Galois representations with large Iwasawa (lambda )-invariant","authors":"Anwesh Ray","doi":"10.1007/s40316-023-00212-5","DOIUrl":"10.1007/s40316-023-00212-5","url":null,"abstract":"<div><p>Let <span>(pge 5)</span> be a prime. We construct modular Galois representations for which the <span>(mathbb {Z}_p)</span>-corank of the <i>p</i>-primary Selmer group (i.e., its <span>(lambda )</span>-invariant) over the cyclotomic <span>(mathbb {Z}_p)</span>-extension is large. More precisely, for any natural number <i>n</i>, one constructs a modular Galois representation such that the associated <span>(lambda )</span>-invariant is <span>(ge n)</span>. The method is based on the study of congruences between modular forms, and leverages results of Greenberg and Vatsal. Given a modular form <span>(f_1)</span> satisfying suitable conditions, one constructs a congruent modular form <span>(f_2)</span> for which the <span>(lambda )</span>-invariant of the Selmer group is large. A key ingredient in acheiving this is the Galois theoretic lifting result of Fakhruddin–Khare–Patrikis, which extends previous work of Ramakrishna. The results are illustrated by explicit examples.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"48 1","pages":"253 - 268"},"PeriodicalIF":0.5,"publicationDate":"2023-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48369166","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
Functional equations for supersingular abelian varieties over ({textbf{Z}}_p^2)-extensions $$｛textbf｛Z｝｝_p^2$$Zp2-扩展上的超奇异阿贝尔变种的函数方程
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2023-01-13 DOI: 10.1007/s40316-022-00210-z
Cédric Dion
{"title":"Functional equations for supersingular abelian varieties over ({textbf{Z}}_p^2)-extensions","authors":"Cédric Dion","doi":"10.1007/s40316-022-00210-z","DOIUrl":"10.1007/s40316-022-00210-z","url":null,"abstract":"<div><p>Let <i>K</i> be an imaginary quadratic field and <span>(K_infty )</span> be the <span>({textbf{Z}}_p^2)</span>-extension of <i>K</i>. Answering a question of Ahmed and Lim, we show that the Pontryagin dual of the Selmer group over <span>(K_infty )</span> associated to a supersingular polarized abelian variety admits an algebraic functional equation. The proof uses the theory of <span>(Gamma )</span>-system developed by Lai, Longhi, Tan and Trihan. We also show the algebraic functional equation holds for Sprung’s chromatic Selmer groups of supersingular elliptic curves along <span>(K_infty )</span>.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"48 1","pages":"221 - 251"},"PeriodicalIF":0.5,"publicationDate":"2023-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47351986","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 adjoint Bloch–Kato Selmer groups for (textrm{GSp}_{2g}) 关于$$textrm的伴随Bloch–Kato-Selmer群{GSp}_｛2g｝$$
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2022-11-19 DOI: 10.1007/s40316-022-00209-6
Ju-Feng Wu
{"title":"On adjoint Bloch–Kato Selmer groups for (textrm{GSp}_{2g})","authors":"Ju-Feng Wu","doi":"10.1007/s40316-022-00209-6","DOIUrl":"10.1007/s40316-022-00209-6","url":null,"abstract":"<div><p>We study the adjoint Bloch–Kato Selmer groups attached to a classical point in the cuspidal eigenvariety associated with <span>(textrm{GSp}_{2g})</span>. Our strategy is based on the study of families of Galois representations on the eigenvariety, which is inspired by the book of J. Bellaiche and G. Chenevier.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"48 1","pages":"187 - 220"},"PeriodicalIF":0.5,"publicationDate":"2022-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40316-022-00209-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43513596","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
Flexibility of Steklov eigenvalues via boundary homogenisation 通过边界均质化实现斯特克洛夫特征值的灵活性
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2022-11-09 DOI: 10.1007/s40316-022-00207-8
Mikhail Karpukhin, Jean Lagacé
{"title":"Flexibility of Steklov eigenvalues via boundary homogenisation","authors":"Mikhail Karpukhin,&nbsp;Jean Lagacé","doi":"10.1007/s40316-022-00207-8","DOIUrl":"10.1007/s40316-022-00207-8","url":null,"abstract":"<div><p>Recently, D. Bucur and M. Nahon used boundary homogenisation to show the remarkable flexibility of Steklov eigenvalues of planar domains. In the present paper we extend their result to higher dimensions and to arbitrary manifolds with boundary, even though in those cases the boundary does not generally exhibit any periodic structure. Our arguments use a framework of variational eigenvalues and provide a different proof of the original results. Furthermore, we present an application of this flexibility to the optimisation of Steklov eigenvalues under perimeter constraint. It is proved that the best upper bound for normalised Steklov eigenvalues of surfaces of genus zero and any fixed number of boundary components can always be saturated by planar domains. This is the case even though any actual maximisers (except for simply connected surfaces) are always far from being planar themselves. In particular, it yields sharp upper bound for the first Steklov eigenvalue of doubly connected planar domains.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"48 1","pages":"175 - 186"},"PeriodicalIF":0.5,"publicationDate":"2022-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40316-022-00207-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142410866","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 anticyclotomic Iwasawa main conjecture for Hilbert modular forms of parallel weights 关于平行权Hilbert模形式的反气旋Iwasawa主猜想
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2022-11-09 DOI: 10.1007/s40316-022-00208-7
Haining Wang
{"title":"On the anticyclotomic Iwasawa main conjecture for Hilbert modular forms of parallel weights","authors":"Haining Wang","doi":"10.1007/s40316-022-00208-7","DOIUrl":"10.1007/s40316-022-00208-7","url":null,"abstract":"<div><p>In this article, we study the Iwasawa theory for Hilbert modular forms over the anticyclotomic extension of a CM field. We prove an one-sided divisibility result toward the Iwasawa main conjecture in this setting. The proof relies on the first and second reciprocity laws relating theta elements to Heegner point Euler systems on Shimura curves. As a by-product we also prove a result towards the rank 0 case of certain Bloch–Kato conjecture and a parity conjecture.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"47 1","pages":"195 - 248"},"PeriodicalIF":0.5,"publicationDate":"2022-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40316-022-00208-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47267030","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: 3
Special issues in honour of Bernadette Perrin-Riou 纪念伯纳黛特·佩林·里欧的特刊
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2022-09-21 DOI: 10.1007/s40316-022-00206-9
Henri Darmon, Adrian Iovita, Antonio Lei
{"title":"Special issues in honour of Bernadette Perrin-Riou","authors":"Henri Darmon,&nbsp;Adrian Iovita,&nbsp;Antonio Lei","doi":"10.1007/s40316-022-00206-9","DOIUrl":"10.1007/s40316-022-00206-9","url":null,"abstract":"","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"46 2","pages":"227 - 229"},"PeriodicalIF":0.5,"publicationDate":"2022-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44615662","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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