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The total Betti number of the independence complex of ternary graphs 三元图的独立复的总贝蒂数
1区 数学
Journal of the European Mathematical Society Pub Date : 2023-09-15 DOI: 10.4171/jems/1378
Wentao Zhang, Hehui Wu
{"title":"The total Betti number of the independence complex of ternary graphs","authors":"Wentao Zhang, Hehui Wu","doi":"10.4171/jems/1378","DOIUrl":"https://doi.org/10.4171/jems/1378","url":null,"abstract":"Given a graph $G$, the independence complex $I(G)$ is the simplicial complex whose faces are the independent sets of $V(G)$. Let $tilde{b}_i$ denote the $i$-th reduced Betti number of $I(G)$, and let $b(G)$ denote the sum of the $tilde{b}_i(G)$’s. A graph is ternary if it does not contain induced cycles with length divisible by 3. Kalai and Meshulam conjectured that $b(G)le 1$ whenever $G$ is ternary. We prove this conjecture. This extends a recent result proved by Chudnovsky, Scott, Seymour and Spirkl that for any ternary graph $G$, the number of independent sets with even cardinality and the number of independent sets with odd cardinality differ by at most 1.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135393560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Frobenian multiplicative functions and rational points in fibrations 颤振中的Frobenian乘法函数和有理点
1区 数学
Journal of the European Mathematical Society Pub Date : 2023-09-15 DOI: 10.4171/jems/1374
Daniel Loughran, Lilian Matthiesen
{"title":"Frobenian multiplicative functions and rational points in fibrations","authors":"Daniel Loughran, Lilian Matthiesen","doi":"10.4171/jems/1374","DOIUrl":"https://doi.org/10.4171/jems/1374","url":null,"abstract":"We consider the problem of counting the number of varieties in a family over $mathbb{Q}$ with a rational point. We obtain lower bounds for this counting problem for some families over $mathbb{P}^1$, even if the Hasse principle fails. We also obtain sharp results for some multinorm equations and for specialisations of certain Brauer group elements on higher-dimensional projective spaces, where we answer some cases of a question of Serre. Our techniques come from arithmetic geometry and additive combinatorics.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135353680","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 7
The Manin constant and the modular degree 马宁常数和模度
1区 数学
Journal of the European Mathematical Society Pub Date : 2023-09-14 DOI: 10.4171/jems/1367
Kestutis Cesnavicius, Michael Neururer, Abhishek Saha
{"title":"The Manin constant and the modular degree","authors":"Kestutis Cesnavicius, Michael Neururer, Abhishek Saha","doi":"10.4171/jems/1367","DOIUrl":"https://doi.org/10.4171/jems/1367","url":null,"abstract":"The Manin constant $c$ of an elliptic curve $E$ over $mathbb{Q}$ is the nonzero integer that scales the differential $omega_f$ determined by the normalized newform $f$ associated to $E$ into the pullback of a Néron differential under a minimal parametrization $phicolon X_0(N)mathbb{Q} twoheadrightarrow E$. Manin conjectured that $c = pm 1$ for optimal parametrizations, and we prove that in general $c mid deg(phi)$ under a minor assumption at $2$ and $3$ that is not needed for cube-free $N$ or for parametrizations by $X_1(N)mathbb{Q}$. Since $c$ is supported at the additive reduction primes, which need not divide $deg(phi)$, this improves the status of the Manin conjecture for many $E$. Our core result that gives this divisibility is the containment $omega_f in H^0(X_0(N), Omega)$, which we establish by combining automorphic methods with techniques from arithmetic geometry; here the modular curve $X_0(N)$ is considered over $mathbb{Z}$ and $Omega$ is its relative dualizing sheaf over $mathbb{Z}$. We reduce this containment to $p$-adic bounds on denominators of the Fourier expansions of $f$ at all the cusps of $X_0(N)_mathbb{C}$ and then use the recent basic identity for the $p$-adic Whittaker newform to establish stronger bounds in the more general setup of newforms of weight $k$ on $X_0(N)$. To overcome obstacles at $2$ and $3$, we analyze nondihedral supercuspidal representations of $operatorname{GL}_2(mathbb{Q}2)$ and exhibit new cases in which $X_0(N)mathbb{Z}$ has rational singularities.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135488731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 Arithmetic Fundamental Lemma conjecture over a general $p$-adic field 一般$p$进域上的算术基本引理猜想
1区 数学
Journal of the European Mathematical Society Pub Date : 2023-09-14 DOI: 10.4171/jems/1375
A. Mihatsch, W. Zhang
{"title":"On the Arithmetic Fundamental Lemma conjecture over a general $p$-adic field","authors":"A. Mihatsch, W. Zhang","doi":"10.4171/jems/1375","DOIUrl":"https://doi.org/10.4171/jems/1375","url":null,"abstract":"We prove the Arithmetic Fundamental Lemma conjecture over a general $p$-adic field with odd residue cardinality $qgeq dim V$. Our strategy is similar to the one used by the second author in his proof of the AFL over $mathbb{Q}_p$, but only requires the modularity of divisor generating series on the Shimura variety (as opposed to its integral model). The resulting increase in flexibility allows us to work over an arbitrary base field. To carry out our strategy, we also generalize results of Howard (2012) on CM cycle intersection and of Ehlen–Sankaran (2018) on Green function comparison from $mathbb{Q}$ to general totally real base fields.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134909946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 5
Volume entropy semi-norm and systolic volume semi-norm 体积熵半范数和收缩体积半范数
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2023-08-03 DOI: 10.4171/jems/1370
I. Babenko, S. Sabourau
{"title":"Volume entropy semi-norm and systolic volume semi-norm","authors":"I. Babenko, S. Sabourau","doi":"10.4171/jems/1370","DOIUrl":"https://doi.org/10.4171/jems/1370","url":null,"abstract":"We introduce the volume entropy semi-norm and the systolic volume semi-norm in real homology and show that they satisfy functorial properties similar to the ones of the simplicial volume. Along the way, we also establish a roughly optimal upper bound on the systolic volume of the multiples of any homology class. Finally, we prove that the volume entropy semi-norm, the systolic volume semi-norm and the simplicial volume semi-norm are equivalent in every dimension.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74219226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Deletion-contraction triangles for Hausel–Proudfoot varieties Hausel-Proudfoot变种的删除-收缩三角形
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2023-08-03 DOI: 10.4171/jems/1369
Zuszsanna Dancso, M. McBreen, V. Shende
{"title":"Deletion-contraction triangles for Hausel–Proudfoot varieties","authors":"Zuszsanna Dancso, M. McBreen, V. Shende","doi":"10.4171/jems/1369","DOIUrl":"https://doi.org/10.4171/jems/1369","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85357840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Statistical reconstruction of the GFF and KT transition GFF和KT转换的统计重建
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2023-08-02 DOI: 10.4171/jems/1288
C. Garban, Avelio Sepúlveda
{"title":"Statistical reconstruction of the GFF and KT transition","authors":"C. Garban, Avelio Sepúlveda","doi":"10.4171/jems/1288","DOIUrl":"https://doi.org/10.4171/jems/1288","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72663523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
The structure and number of Erdős covering systems Erdős覆盖系统的结构和数量
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2023-06-14 DOI: 10.4171/jems/1357
P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe, M. Tiba
{"title":"The structure and number of Erdős covering systems","authors":"P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe, M. Tiba","doi":"10.4171/jems/1357","DOIUrl":"https://doi.org/10.4171/jems/1357","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82081035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Nonuniqueness in law of stochastic 3D Navier–Stokes equations 三维随机Navier-Stokes方程的非唯一性
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2023-06-12 DOI: 10.4171/jems/1360
M. Hofmanová, Rongchan Zhu, Xiangchan Zhu
{"title":"Nonuniqueness in law of stochastic 3D Navier–Stokes equations","authors":"M. Hofmanová, Rongchan Zhu, Xiangchan Zhu","doi":"10.4171/jems/1360","DOIUrl":"https://doi.org/10.4171/jems/1360","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88627010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Elliptic surfaces and intersections of adelic $mathbb{R}$-divisors -因子的椭圆曲面与交点
1区 数学
Journal of the European Mathematical Society Pub Date : 2023-06-07 DOI: 10.4171/jems/1340
Laura DeMarco, Niki Myrto Mavraki
{"title":"Elliptic surfaces and intersections of adelic $mathbb{R}$-divisors","authors":"Laura DeMarco, Niki Myrto Mavraki","doi":"10.4171/jems/1340","DOIUrl":"https://doi.org/10.4171/jems/1340","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135402488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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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