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Annales Mathematiques du Quebec最新文献

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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
(pmb {mathscr {L}})-invariants of Artin motives （pmb｛mathscr｛L｝｝）-Artin动机的不变量
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2022-07-27 DOI: 10.1007/s40316-022-00201-0
Mladen Dimitrov, Alexandre Maksoud
{"title":"(pmb {mathscr {L}})-invariants of Artin motives","authors":"Mladen Dimitrov,&nbsp;Alexandre Maksoud","doi":"10.1007/s40316-022-00201-0","DOIUrl":"10.1007/s40316-022-00201-0","url":null,"abstract":"<div><h2>R'esum'e</h2><div><p>We compute Benois <span>({mathscr {L}})</span>-invariants of weight 1 cuspforms and of their adjoint representations and show how this extends Gross’ <i>p</i>-adic regulator to Artin motives which are not critical in the sense of Deligne. Benois’ construction depends on the choice of a regular submodule which is well understood when the representation is <i>p</i>-regular, as it then amounts to the choice of a “motivic” <i>p</i>-refinement. The situation is dramatically different in the <i>p</i>-irregular case, where the regular submodules are parametrized by a flag variety and thus depend on continuous parameters. We are nevertheless able to show in some examples, how Hida theory and the geometry of the eigencurve can be used to detect a finite number of choices of arithmetic and “mixed-motivic” significance.</p></div></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"47 1","pages":"49 - 71"},"PeriodicalIF":0.5,"publicationDate":"2022-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50517678","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
$$pmb {mathscr {L}}$$ L -invariants of Artin motives $$pmb｛mathscr｛L｝｝$$L-阿廷动机的不变量
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2022-07-27 DOI: 10.1007/s40316-022-00201-0
Mladen Dimitrov, Alexandre Maksoud
{"title":"\u0000 \u0000 \u0000 \u0000 $$pmb {mathscr {L}}$$\u0000 \u0000 \u0000 L\u0000 \u0000 \u0000 -invariants of Artin motives","authors":"Mladen Dimitrov, Alexandre Maksoud","doi":"10.1007/s40316-022-00201-0","DOIUrl":"https://doi.org/10.1007/s40316-022-00201-0","url":null,"abstract":"","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"47 1","pages":"49-71"},"PeriodicalIF":0.5,"publicationDate":"2022-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49183393","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
Hardy and Littlewood theorems and the Bergman distance Hardy和Littlewood定理与Bergman距离
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2022-07-19 DOI: 10.1007/s40316-022-00205-w
Marijan Marković
{"title":"Hardy and Littlewood theorems and the Bergman distance","authors":"Marijan Marković","doi":"10.1007/s40316-022-00205-w","DOIUrl":"10.1007/s40316-022-00205-w","url":null,"abstract":"<p>We obtain non-Euclidean versions of classical theorems due to Hardy and Littlewood concerning smoothness of the boundary function of an analytic mapping on the unit disk with an appropriate growth condition.</p>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"48 1","pages":"143 - 156"},"PeriodicalIF":0.5,"publicationDate":"2022-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49468781","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
Normal integral bases and Gaussian periods in the simplest cubic fields 最简三次场中的正规积分基和高斯周期
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2022-07-19 DOI: 10.1007/s40316-022-00204-x
Yu Hashimoto, Miho Aoki
{"title":"Normal integral bases and Gaussian periods in the simplest cubic fields","authors":"Yu Hashimoto,&nbsp;Miho Aoki","doi":"10.1007/s40316-022-00204-x","DOIUrl":"10.1007/s40316-022-00204-x","url":null,"abstract":"<div><p>We give all normal integral bases for the simplest cubic field <span>(L_n)</span> generated by the roots of Shanks’ cubic polynomial when these bases exist, that is, <span>(L_n/{mathbb {Q}})</span> is tamely ramified. Furthermore, as an application of the result, we give an explicit relation between the roots of Shanks’ cubic polynomial and the Gaussian periods of <span>(L_n)</span> in the case that <span>(L_n/{mathbb {Q}})</span> is tamely ramified, which is a generalization of the work of Lehmer, Châtelet and Lazarus in the case that the conductor of <span>(L_n)</span> is equal to <span>(n^2+3n+9)</span>.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"48 1","pages":"157 - 173"},"PeriodicalIF":0.5,"publicationDate":"2022-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45301596","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
(p^infty )-Selmer groups and rational points on CM elliptic curves $$p^infty$$-CM椭圆曲线上的Selmer群和有理点
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2022-07-08 DOI: 10.1007/s40316-022-00203-y
Ashay Burungale, Francesc Castella, Christopher Skinner, Ye Tian
{"title":"(p^infty )-Selmer groups and rational points on CM elliptic curves","authors":"Ashay Burungale,&nbsp;Francesc Castella,&nbsp;Christopher Skinner,&nbsp;Ye Tian","doi":"10.1007/s40316-022-00203-y","DOIUrl":"10.1007/s40316-022-00203-y","url":null,"abstract":"<div><h2>R'esum'e</h2><div><p>Let <span>(E/{mathbb {Q}})</span> be a CM elliptic curve and <i>p</i> a prime of good ordinary reduction for <i>E</i>. We show that if <span>(text {Sel}_{p^infty }(E/{mathbb {Q}}))</span> has <span>({mathbb {Z}}_p)</span>-corank one, then <span>(E({mathbb {Q}}))</span> has a point of infinite order. The non-torsion point arises from a Heegner point, and thus <span>({{,mathrm{ord},}}_{s=1}L(E,s)=1)</span>, yielding a <i>p</i>-converse to a theorem of Gross–Zagier, Kolyvagin, and Rubin in the spirit of [49, 54]. For <span>(p&gt;3)</span>, this gives a new proof of the main result of [12], which our approach extends to all primes. The approach generalizes to CM elliptic curves over totally real fields [4].</p></div></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"46 2","pages":"325 - 346"},"PeriodicalIF":0.5,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40316-022-00203-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42029525","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
Eggbeater dynamics on symplectic surfaces of genus 2 and 3 2和3属辛表面上的打蛋机动力学
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2022-07-08 DOI: 10.1007/s40316-022-00202-z
Arnon Chor
{"title":"Eggbeater dynamics on symplectic surfaces of genus 2 and 3","authors":"Arnon Chor","doi":"10.1007/s40316-022-00202-z","DOIUrl":"10.1007/s40316-022-00202-z","url":null,"abstract":"<div><p>The group <span>(Ham(M,omega ))</span> of all Hamiltonian diffeomorphisms of a symplectic manifold <span>((M,omega ))</span> plays a central role in symplectic geometry. This group is endowed with the Hofer metric. In this paper we study two aspects of the geometry of <span>(Ham(M,omega ))</span>, in the case where <i>M</i> is a closed surface of genus 2 or 3. First, we prove that there exist diffeomorphisms in <span>(Ham(M,omega ))</span> arbitrarily far from being a <i>k</i>-th power, with respect to the metric, for any <span>(k ge 2)</span>. This part generalizes previous work by Polterovich and Shelukhin. Second, we show that the free group on two generators embeds into the asymptotic cone of <span>(Ham(M,omega ))</span>. This part extends previous work by Alvarez-Gavela et al. Both extensions are based on two results from geometric group theory regarding incompressibility of surface embeddings.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"48 1","pages":"113 - 142"},"PeriodicalIF":0.5,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44359314","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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