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Expositiones Mathematicae最新文献

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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, Ziyang Gao, Pierre Parent, 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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
On Ramanujan’s continued fractions of order twenty-four 关于拉马努金的24阶连分数
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2023-08-21 DOI: 10.1016/j.exmath.2023.08.003
Shraddha Rajkhowa, Nipen Saikia
{"title":"On Ramanujan’s continued fractions of order twenty-four","authors":"Shraddha Rajkhowa,&nbsp;Nipen Saikia","doi":"10.1016/j.exmath.2023.08.003","DOIUrl":"10.1016/j.exmath.2023.08.003","url":null,"abstract":"<div><p>Two continued fractions <span><math><mrow><mi>U</mi><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>V</mi><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow></mrow></math></span><span> of order twenty-four are obtained from a general continued fraction identity of Ramanujan. Some theta-function and modular identities for </span><span><math><mrow><mi>U</mi><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>V</mi><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow></mrow></math></span> are established to prove general theorems for the explicit evaluations of <span><math><mrow><mi>U</mi><mrow><mo>(</mo><mo>±</mo><mi>q</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>V</mi><mrow><mo>(</mo><mo>±</mo><mi>q</mi><mo>)</mo></mrow></mrow></math></span>. From the theta-function identities of <span><math><mrow><mi>U</mi><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>V</mi><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow></mrow></math></span>, three colour partition identities are derived as application to partition theory of integer. Further, <span><math><mn>2</mn></math></span>-, <span><math><mn>4</mn></math></span>- and <span><math><mn>8</mn></math></span>-dissection formulas are established for the continued fractions <span><math><mrow><msup><mrow><mi>U</mi></mrow><mrow><mo>∗</mo></mrow></msup><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow><mo>≔</mo><msup><mrow><mi>q</mi></mrow><mrow><mo>−</mo><mn>5</mn><mo>/</mo><mn>2</mn></mrow></msup><mi>U</mi><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><msup><mrow><mi>V</mi></mrow><mrow><mo>∗</mo></mrow></msup><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow><mo>≔</mo><msup><mrow><mi>q</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mi>V</mi><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow></mrow></math></span>, and their reciprocals.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42408513","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
Composition of Bhargava’s cubes over number fields 巴尔伽瓦立方体在数域上的组合
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2023-08-19 DOI: 10.1016/j.exmath.2023.08.002
Kristýna Zemková
{"title":"Composition of Bhargava’s cubes over number fields","authors":"Kristýna Zemková","doi":"10.1016/j.exmath.2023.08.002","DOIUrl":"10.1016/j.exmath.2023.08.002","url":null,"abstract":"<div><p><span><span>In this paper, the composition of Bhargava’s cubes is generalized to the ring of integers of a number field of narrow class number one, excluding the case of totally imaginary number fields. The exclusion of the latter case arises from the nonexistence of a </span>bijection between (classes of) binary </span>quadratic forms and an ideal class group. This problem, together with a related mistake in another paper of the author, is addressed in the appendix.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44892435","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
The Riemann–Roch theorem for the Adams operations Adams运算的Riemann-Roch定理
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2023-08-01 DOI: 10.1016/j.exmath.2023.07.002
A. Navarro , J. Navarro
{"title":"The Riemann–Roch theorem for the Adams operations","authors":"A. Navarro ,&nbsp;J. Navarro","doi":"10.1016/j.exmath.2023.07.002","DOIUrl":"10.1016/j.exmath.2023.07.002","url":null,"abstract":"<div><p>We prove the classical Riemann–Roch theorems for the Adams operations <span><math><mrow><mspace></mspace><msup><mrow><mi>ψ</mi></mrow><mrow><mi>j</mi></mrow></msup><mspace></mspace></mrow></math></span> on <span><math><mi>K</mi></math></span>-theory: a statement with coefficients on <span><math><mrow><mi>Z</mi><mrow><mo>[</mo><msup><mrow><mi>j</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>]</mo></mrow></mrow></math></span><span><span>, that holds for arbitrary projective morphisms, as well as another statement with </span>integral coefficients<span>, that is valid for closed immersions. In presence of rational coefficients, we also analyze the relation between the corresponding Riemann–Roch formula for one Adams operation and the analogous formula for the Chern character. To do so, we complete the elementary exposition of the work of Panin–Smirnov that was initiated by the first author in a previous paper. Their notion of oriented cohomology<span> theory on algebraic varieties allows to use classical arguments to prove general and neat statements, which imply all the aforementioned results as particular cases.</span></span></span></p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44076407","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 Briançon–Skoda theorem for foliations 关于叶理的BriançOn–Skoda定理
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2023-07-20 DOI: 10.1016/j.exmath.2023.07.001
Arturo Fernández-Pérez , Evelia R. García Barroso , Nancy Saravia-Molina
{"title":"On Briançon–Skoda theorem for foliations","authors":"Arturo Fernández-Pérez ,&nbsp;Evelia R. García Barroso ,&nbsp;Nancy Saravia-Molina","doi":"10.1016/j.exmath.2023.07.001","DOIUrl":"10.1016/j.exmath.2023.07.001","url":null,"abstract":"<div><p>We generalize Mattei’s result relative to the Briançon–Skoda theorem for foliations to the family of foliations of the second type. We use this generalization to establish relationships between the Milnor and Tjurina numbers of foliations of second type, inspired by the results obtained by Liu for complex hypersurfaces and we determine a lower bound for the global Tjurina number of an algebraic curve.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43076398","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 an identity of Sylvester 以西尔维斯特的身份
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2023-06-25 DOI: 10.1016/j.exmath.2023.06.003
Bogdan Nica
{"title":"On an identity of Sylvester","authors":"Bogdan Nica","doi":"10.1016/j.exmath.2023.06.003","DOIUrl":"10.1016/j.exmath.2023.06.003","url":null,"abstract":"<div><p>We discuss an algebraic identity, due to Sylvester, as well as related algebraic identities and applications.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44956206","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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