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$mathbb{C}$-motivic modular forms $mathbb{C}$-动机模块形式
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-11-09 DOI: 10.4171/jems/1171
Bogdan Gheorghe, Daniel Isaksen, Achim Krause, N. Ricka
{"title":"$mathbb{C}$-motivic modular forms","authors":"Bogdan Gheorghe, Daniel Isaksen, Achim Krause, N. Ricka","doi":"10.4171/jems/1171","DOIUrl":"https://doi.org/10.4171/jems/1171","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2021-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85334215","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
Landau–Ginzburg mirror symmetry conjecture 朗道-金兹堡镜像对称猜想
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-11-05 DOI: 10.4171/jems/1155
Weiqiang He, Si Li, Yefeng Shen, Rachel Webb
{"title":"Landau–Ginzburg mirror symmetry conjecture","authors":"Weiqiang He, Si Li, Yefeng Shen, Rachel Webb","doi":"10.4171/jems/1155","DOIUrl":"https://doi.org/10.4171/jems/1155","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2021-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79568127","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
Summability of the coefficients of a multilinear form 多线性形式的系数的可和性
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-07-21 DOI: 10.4171/JEMS/1109
F. Bayart
{"title":"Summability of the coefficients of a multilinear form","authors":"F. Bayart","doi":"10.4171/JEMS/1109","DOIUrl":"https://doi.org/10.4171/JEMS/1109","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72713098","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: 6
On the distribution of ${Cl}(K)[l^infty]$ for degree $l$ cyclic fields 关于次$l$循环场${Cl}(K)[l^infty]$的分布
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-07-20 DOI: 10.4171/JEMS/1112
P. Koymans, Carlo Pagano
{"title":"On the distribution of ${Cl}(K)[l^infty]$ for degree $l$ cyclic fields","authors":"P. Koymans, Carlo Pagano","doi":"10.4171/JEMS/1112","DOIUrl":"https://doi.org/10.4171/JEMS/1112","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2021-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85013265","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
On a class number formula of Hurwitz 关于Hurwitz的一个类数公式
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-05-25 DOI: 10.4171/JEMS/1097
W. Duke, Ö. Imamoḡlu, Á. Tóth
{"title":"On a class number formula of Hurwitz","authors":"W. Duke, Ö. Imamoḡlu, Á. Tóth","doi":"10.4171/JEMS/1097","DOIUrl":"https://doi.org/10.4171/JEMS/1097","url":null,"abstract":"In a little-known paper Hurwitz gave an infinite series representation of the class number for positive definite binary quadratic forms. In this paper we give a similar formula in the indefinite case. We also give a simple proof of Hurwitz’s formula and indicate some extensions.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2021-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75556520","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: 2
The number of $D_4$-fields ordered by conductor 由导体排序的$D_4$-字段的数目
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-05-04 DOI: 10.4171/JEMS/1070
S. A. Altug, A. Shankar, Ila Varma, Kevin H. Wilson
{"title":"The number of $D_4$-fields ordered by conductor","authors":"S. A. Altug, A. Shankar, Ila Varma, Kevin H. Wilson","doi":"10.4171/JEMS/1070","DOIUrl":"https://doi.org/10.4171/JEMS/1070","url":null,"abstract":"We consider families of quartic number fields whose normal closures over Q have Galois group isomorphic to D4, the symmetries of a square. To any such field L, one can associate the Artin conductor of the corresponding 2-dimensional irreducible Galois representation with image D4. We determine the asymptotic number of such D4-quartic fields ordered by conductor, and compute the leading term explicitly as a mass formula, verifying heuristics of Kedlaya and Wood. Additionally, we are able to impose any local splitting conditions at any finite number of primes (sometimes, at an infinite number of primes), and as a consequence, we also compute the asymptotic number of order 4 elements in class groups and narrow class groups of quadratic fields ordered by discriminant. Traditionally, there have been two approaches to counting quartic fields, using arithmetic invariant theory in combination with geometry-of-number techniques, and applying Kummer theory together with L-function methods. Both of these strategies fall short in the case of D4-quartic fields ordered by conductor since counting quartic fields containing a quadratic subfield with large discriminant is difficult. However, when ordering by conductor, we utilize additional algebraic structure arising from the outer automorphism of D4 combined with both approaches mentioned above to obtain exact asymptotics.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2021-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75816555","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: 16
Global Frobenius liftability I 全局Frobenius可举性1
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-04-14 DOI: 10.4171/JEMS/1063
Piotr Achinger, J. Witaszek, Maciej Zdanowicz
{"title":"Global Frobenius liftability I","authors":"Piotr Achinger, J. Witaszek, Maciej Zdanowicz","doi":"10.4171/JEMS/1063","DOIUrl":"https://doi.org/10.4171/JEMS/1063","url":null,"abstract":"We formulate a conjecture characterizing smooth projective varieties in positive characteristic whose Frobenius morphism can be lifted modulo $p^2$ - we expect that such varieties, after a finite 'etale cover, admit a toric fibration over an ordinary abelian variety. We prove that this assertion implies a conjecture of Occhetta and Wi'sniewski, which states that in characteristic zero a smooth image of a projective toric variety is a toric variety. To this end we analyse the behaviour of toric varieties in families showing some generization and specialization results. Furthermore, we prove a positive characteristic analogue of Winkelmann's theorem on varieties with trivial logarithmic tangent bundle (generalising a result of Mehta-Srinivas), and thus obtaining an important special case of our conjecture. Finally, using deformations of rational curves we verify our conjecture for homogeneous spaces, solving a problem posed by Buch-Thomsen-Lauritzen-Mehta.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2021-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81273535","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: 9
A set of positive Gaussian measure with uniformly zero density everywhere. 一组处处均匀密度为零的正高斯测度。
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-03-25 DOI: 10.4171/JEMS/1058
D. Preiss, E. Riss, J. Tiser
{"title":"A set of positive Gaussian measure with uniformly zero density everywhere.","authors":"D. Preiss, E. Riss, J. Tiser","doi":"10.4171/JEMS/1058","DOIUrl":"https://doi.org/10.4171/JEMS/1058","url":null,"abstract":"Existing negative results on invalidity of analogues of classical Density and Differentiation Theorems in infinite dimensional spaces are considerably strengthened by a construction of a Gaussian measure γ on a separable Hilbert space H for which the Density Theorem fails uniformly, i.e., there is a set M ⊂ H of positive γ-measure such that lim rց0 sup x∈H γ(B(x, r) ∩M) γB(x, r) = 0.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2021-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75437082","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
Infinite stable graphs with large chromatic number II 具有大色数的无限稳定图II
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-03-25 DOI: 10.4171/jems/1352
Yatir Halevi, Itay Kaplan, S. Shelah
{"title":"Infinite stable graphs with large chromatic number II","authors":"Yatir Halevi, Itay Kaplan, S. Shelah","doi":"10.4171/jems/1352","DOIUrl":"https://doi.org/10.4171/jems/1352","url":null,"abstract":"We prove a version of the strong Taylor's conjecture for stable graphs: if $G$ is a stable graph whose chromatic number is strictly greater than $beth_2(aleph_0)$ then $G$ contains all finite subgraphs of Sh$_n(omega)$ and thus has elementary extensions of unbounded chromatic number. This completes the picture from our previous work. The main new model theoretic ingredient is a generalization of the classical construction of Ehrenfeucht-Mostowski models to an infinitary setting, giving a new characterization of stability.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2021-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90647866","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 values of the Dedekind–Rademacher cocycle at real multiplication points Dedekind-Rademacher循环在实乘法点处的值
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-03-03 DOI: 10.4171/jems/1344
H. Darmon, A. Pozzi, Jan Vonk
{"title":"The values of the Dedekind–Rademacher cocycle at real multiplication points","authors":"H. Darmon, A. Pozzi, Jan Vonk","doi":"10.4171/jems/1344","DOIUrl":"https://doi.org/10.4171/jems/1344","url":null,"abstract":"The values of the so-called {em Dedekind--Rademacher cocycle} at certain real quadratic arguments are shown to be global $p$-units in the narrow Hilbert class field of the associated real quadratic field, as predicted by conjectures of Darmon, Dasgupta, and Vonk. The strategy for proving this result combines an approach of Darmon-Pozzi-Vonk with one crucial extra ingredient: the study of infinitesimal deformations of irregular Hilbert Eisenstein series of weight one in the anti-parallel direction, building on the techniques in earlier work of Betina, Dimitrov, and Pozzi.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2021-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75770968","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: 18
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