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Expositiones Mathematicae最新文献

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A K3 surface related to Leonardo Pisano’s work on congruent numbers 与Leonardo Pisano关于全等数的研究有关的K3曲面
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2023-09-01 DOI: 10.1016/j.exmath.2023.03.003
Martin Djukanović, Jaap Top
{"title":"A K3 surface related to Leonardo Pisano’s work on congruent numbers","authors":"Martin Djukanović,&nbsp;Jaap Top","doi":"10.1016/j.exmath.2023.03.003","DOIUrl":"10.1016/j.exmath.2023.03.003","url":null,"abstract":"<div><p>This note recalls an early 13th century result on congruent numbers by Leonardo Pisano (“Fibonacci”), and shows how it relates to a specific much studied K3 surface and to an elliptic fibration on this surface. As an aside, the discussion reveals how, via explicit maps of degree two, the surface is covered by the Fermat quartic surface and also covers one of the two famous ‘most algebraic K3 surfaces’.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"41 3","pages":"Pages 566-576"},"PeriodicalIF":0.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41595977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An overview on problems of Unlikely Intersections in families of abelian varieties 阿贝尔变种族中不可能相交问题综述
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2023-09-01 DOI: 10.1016/j.exmath.2023.04.003
Laura Capuano
{"title":"An overview on problems of Unlikely Intersections in families of abelian varieties","authors":"Laura Capuano","doi":"10.1016/j.exmath.2023.04.003","DOIUrl":"10.1016/j.exmath.2023.04.003","url":null,"abstract":"<div><p>This short survey is part of a minicourse I gave during the CMI-HIMR Summer School “Unlikely Intersections in Diophantine Geometry” on the Zilber–Pink conjecture, formulated independently by Zilber (2002), Bombieri, Masser and Zannier (1999) in the case of tori and by Pink (2005) in the more general setting of mixed Shimura varieties. This conjecture, which includes in its general formulation many important results in number theory<span>, has been intensively studied by several mathematicians in the past 20 years. We will mainly focus on these problems in the special setting of semiabelian varieties and families of abelian varieties.</span></p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"41 3","pages":"Pages 603-617"},"PeriodicalIF":0.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42436947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Extensions and torsors for finite group schemes 有限群格式的扩张与扭转
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2023-09-01 DOI: 10.1016/j.exmath.2023.02.004
Peter Bruin
{"title":"Extensions and torsors for finite group schemes","authors":"Peter Bruin","doi":"10.1016/j.exmath.2023.02.004","DOIUrl":"10.1016/j.exmath.2023.02.004","url":null,"abstract":"<div><p>We give an explicit description of the category of central extensions of a group scheme by a sheaf of Abelian groups. Based on this, we describe a framework for computing with central extensions of finite locally free commutative group schemes, torsors under such group schemes and groups of isomorphism classes of these objects.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"41 3","pages":"Pages 514-530"},"PeriodicalIF":0.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43076278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Computing the trace of an algebraic point on an elliptic curve 计算椭圆曲线上代数点的轨迹
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2023-09-01 DOI: 10.1016/j.exmath.2023.02.006
Nicolas Mascot , Denis Simon
{"title":"Computing the trace of an algebraic point on an elliptic curve","authors":"Nicolas Mascot ,&nbsp;Denis Simon","doi":"10.1016/j.exmath.2023.02.006","DOIUrl":"10.1016/j.exmath.2023.02.006","url":null,"abstract":"<div><p>We present a simple and efficient algorithm to compute the sum of the algebraic conjugates of a point on an elliptic curve.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"41 3","pages":"Pages 463-474"},"PeriodicalIF":0.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43843514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Problèmes de type André-Oort en pinceau arithmétique 算术笔画中的andre - oort问题
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2023-09-01 DOI: 10.1016/j.exmath.2023.05.004
Rodolphe Richard
{"title":"Problèmes de type André-Oort en pinceau arithmétique","authors":"Rodolphe Richard","doi":"10.1016/j.exmath.2023.05.004","DOIUrl":"10.1016/j.exmath.2023.05.004","url":null,"abstract":"<div><p>Nous proposons une “Conjecture d’André-Oort en pinceau arithmétique”.</p><p>C’est une extension de la conjecture d’André-Oort, disons “classique”, formulée à l’origine par Y. André et F. Oort. La conjecture fait intervenir les modèles entiers des variétés de Shimura.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"41 3","pages":"Pages 618-630"},"PeriodicalIF":0.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43293945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Editorial for special issue in honor of B. Edixhoven (1962-2022) B.Edixhoven纪念特刊编辑（1962-2022）
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2023-09-01 DOI: 10.1016/j.exmath.2023.08.001
Jennifer Balakrishnan, Ziyang Gao, Pierre Parent, Andrei Yafaev
{"title":"Editorial for special issue in honor of B. Edixhoven (1962-2022)","authors":"Jennifer Balakrishnan,&nbsp;Ziyang Gao,&nbsp;Pierre Parent,&nbsp;Andrei Yafaev","doi":"10.1016/j.exmath.2023.08.001","DOIUrl":"10.1016/j.exmath.2023.08.001","url":null,"abstract":"","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"41 3","pages":"Pages 461-462"},"PeriodicalIF":0.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46333260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Geometric Zilber–Pink theorem and the Lawrence–Venkatesh method 几何Zilber-Pink定理与Lawrence-Venkatesh方法
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2023-09-01 DOI: 10.1016/j.exmath.2023.05.001
Gregorio Baldi , Bruno Klingler , Emmanuel Ullmo
{"title":"On the Geometric Zilber–Pink theorem and the Lawrence–Venkatesh method","authors":"Gregorio Baldi ,&nbsp;Bruno Klingler ,&nbsp;Emmanuel Ullmo","doi":"10.1016/j.exmath.2023.05.001","DOIUrl":"10.1016/j.exmath.2023.05.001","url":null,"abstract":"<div><p>Using our recent results on the algebraicity of the Hodge locus for variations of Hodge structures of level at least 3, we improve the results of Lawrence–Venkatesh in direction of the refined Bombieri–Lang conjecture.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"41 3","pages":"Pages 718-722"},"PeriodicalIF":0.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47373732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Rings of tautological forms on moduli spaces of curves 曲线模空间上的同义形式环
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2023-09-01 DOI: 10.1016/j.exmath.2023.02.008
Robin de Jong, Stefan van der Lugt
{"title":"Rings of tautological forms on moduli spaces of curves","authors":"Robin de Jong,&nbsp;Stefan van der Lugt","doi":"10.1016/j.exmath.2023.02.008","DOIUrl":"https://doi.org/10.1016/j.exmath.2023.02.008","url":null,"abstract":"<div><p>We define and study a natural system of tautological rings on the moduli spaces of marked curves at the level of differential forms. We show that certain 2-forms obtained from the natural normal functions on these moduli spaces are tautological. Also we show that rings of tautological forms are always finite dimensional. Finally we characterize the Kawazumi–Zhang invariant as essentially the only smooth function on the moduli space of curves whose Levi form is a tautological form.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"41 3","pages":"Pages 531-565"},"PeriodicalIF":0.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49865976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rational points on Atkin–Lehner quotients of geometrically hyperelliptic Shimura curves 几何超椭圆Shimura曲线Atkin-Lehner商上的有理点
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2023-09-01 DOI: 10.1016/j.exmath.2023.02.005
Oana Padurariu , Ciaran Schembri
{"title":"Rational points on Atkin–Lehner quotients of geometrically hyperelliptic Shimura curves","authors":"Oana Padurariu ,&nbsp;Ciaran Schembri","doi":"10.1016/j.exmath.2023.02.005","DOIUrl":"10.1016/j.exmath.2023.02.005","url":null,"abstract":"<div><p>Guo and Yang give defining equations for all geometrically hyperelliptic Shimura curves <span><math><mrow><msub><mrow><mi>X</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><mi>D</mi><mo>,</mo><mi>N</mi><mo>)</mo></mrow></mrow></math></span>. In this paper we compute the <span><math><mi>Q</mi></math></span>-rational points on the Atkin–Lehner quotients of these curves using a variety of techniques. We also determine which rational points are CM for many of these curves.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"41 3","pages":"Pages 492-513"},"PeriodicalIF":0.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47086175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Rational points on X0+(125) X0+(125)的有理点
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2023-09-01 DOI: 10.1016/j.exmath.2023.02.009
Vishal Arul , J. Steffen Müller
{"title":"Rational points on X0+(125)","authors":"Vishal Arul ,&nbsp;J. Steffen Müller","doi":"10.1016/j.exmath.2023.02.009","DOIUrl":"https://doi.org/10.1016/j.exmath.2023.02.009","url":null,"abstract":"<div><p>We compute the rational points on the Atkin–Lehner quotient <span><math><mrow><msubsup><mrow><mi>X</mi></mrow><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msubsup><mrow><mo>(</mo><mn>125</mn><mo>)</mo></mrow></mrow></math></span> using the quadratic Chabauty method. Our work completes the study of exceptional rational points on the curves <span><math><mrow><msubsup><mrow><mi>X</mi></mrow><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msubsup><mrow><mo>(</mo><mi>N</mi><mo>)</mo></mrow></mrow></math></span> of genus between 2 and 6. Together with the work of several authors, this completes the proof of a conjecture of Galbraith.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"41 3","pages":"Pages 709-717"},"PeriodicalIF":0.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49865974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","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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