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Annales Mathematiques du Quebec最新文献

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(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
Iwasawa theory for (mathrm {GL}_2times mathrm {Res}_{K/mathbb {Q}}mathrm {GL}_1) 解释（mathrm的理论{GL}_2timesmathrm{Res}_｛K/mathbb｛Q｝mathrm{GL}_1（电话铃声）
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2022-06-06 DOI: 10.1007/s40316-022-00197-7
Kâzim Büyükboduk, Antonio Lei
{"title":"Iwasawa theory for (mathrm {GL}_2times mathrm {Res}_{K/mathbb {Q}}mathrm {GL}_1)","authors":"Kâzim Büyükboduk,&nbsp;Antonio Lei","doi":"10.1007/s40316-022-00197-7","DOIUrl":"10.1007/s40316-022-00197-7","url":null,"abstract":"<div><p>Let <i>K</i> be an imaginary quadratic field where the prime <i>p</i> splits. Our goal in this article is to prove results towards the Iwasawa main conjectures for <i>p</i>-nearly-ordinary families associated to <span>(mathrm {GL}_2times mathrm {Res}_{K/mathbb {Q}}mathrm {GL}_1)</span> with a minimal set of assumptions. The main technical input is an improvement on the locally restricted Euler system machinery that allows the treatment of residually reducible cases, which we apply with the Beilinson–Flach Euler system.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"46 2","pages":"347 - 418"},"PeriodicalIF":0.5,"publicationDate":"2022-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40316-022-00197-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50456151","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: 1
The derivative formula of p-adic L-functions for imaginary quadratic fields at trivial zeros 虚二次域在平凡零点处的p进l函数的导数公式
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2022-05-26 DOI: 10.1007/s40316-022-00198-6
Masataka Chida, Ming-Lun Hsieh
{"title":"The derivative formula of p-adic L-functions for imaginary quadratic fields at trivial zeros","authors":"Masataka Chida,&nbsp;Ming-Lun Hsieh","doi":"10.1007/s40316-022-00198-6","DOIUrl":"10.1007/s40316-022-00198-6","url":null,"abstract":"<div><p>The rank one Gross conjecture for Deligne–Ribet <i>p</i>-adic <i>L</i>-functions was solved in works of Darmon-Dasgupta-Pollack and Ventullo by the Eisenstein congruence among Hilbert modular forms. The purpose of this paper is to prove an analogue of the Gross conjecture for the Katz <i>p</i>-adic <i>L</i>-functions attached to imaginary quadratic fields via the congruences between CM forms and non-CM forms. The new ingredient is to apply the <i>p</i>-adic Rankin–Selberg method to construct a non-CM Hida family which is congruent to a Hida family of CM forms at the <span>(1+varepsilon )</span> specialization.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"47 1","pages":"1 - 30"},"PeriodicalIF":0.5,"publicationDate":"2022-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45373264","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: 4
A weighted invariant trace formula 一个加权不变迹公式
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2022-05-25 DOI: 10.1007/s40316-022-00200-1
Tian An Wong
{"title":"A weighted invariant trace formula","authors":"Tian An Wong","doi":"10.1007/s40316-022-00200-1","DOIUrl":"10.1007/s40316-022-00200-1","url":null,"abstract":"<div><p>This paper begins a new approach to the <i>r</i>-trace formula, without removing the nontempered contribution to the spectral side. We first establish an invariant trace formula whose discrete spectral terms are weighted by automorphic <i>L</i>-functions. This involves extending the results of Finis, Lapid, and Müller on the continuity of the coarse expansion of Arthur’s noninvariant trace formula to the refined expansion, and then to the invariant trace formula, while incorporating the use of basic functions at unramified places.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"48 1","pages":"79 - 112"},"PeriodicalIF":0.5,"publicationDate":"2022-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48467646","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 generalization of analytic torsion via differential forms on spaces of metrics 度量空间上解析扭转的微分形式推广
IF 0.5
Annales Mathematiques du Quebec Pub Date : 2022-05-21 DOI: 10.1007/s40316-022-00199-5
Phillip Andreae
{"title":"A generalization of analytic torsion via differential forms on spaces of metrics","authors":"Phillip Andreae","doi":"10.1007/s40316-022-00199-5","DOIUrl":"10.1007/s40316-022-00199-5","url":null,"abstract":"<div><p>We introduce multi-torsion, a spectral invariant generalizing Ray–Singer analytic torsion. We define multi-torsion for compact manifolds with a certain local geometric product structure that gives a bigrading on differential forms. We prove that multi-torsion is metric-independent in a suitable sense. Our definition of multi-torsion is inspired by an interpretation of each of analytic torsion and the eta invariant as a regularized integral of a closed differential form on a space of metrics on a vector bundle or on a space of elliptic operators. We generalize the Stokes’ theorem argument explaining the dependence of torsion and eta on the geometric data used to define them to the local product setting to prove our metric-independence theorem for multi-torsion.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"48 1","pages":"45 - 78"},"PeriodicalIF":0.5,"publicationDate":"2022-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49515704","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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