发布求助
文献互助 智能选刊 最新文献

Commentarii Mathematici Helvetici最新文献

筛选
英文 中文
Moments and interpretations of the Cohen–Lenstra–Martinet heuristics Cohen-Lenstra-Martinet启发式的时刻和解释
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2019-07-25 DOI: 10.4171/cmh/514
Weitong Wang, M. Wood
{"title":"Moments and interpretations of the Cohen–Lenstra–Martinet heuristics","authors":"Weitong Wang, M. Wood","doi":"10.4171/cmh/514","DOIUrl":"https://doi.org/10.4171/cmh/514","url":null,"abstract":"The goal of this paper is to prove theorems that elucidate the Cohen-Lenstra-Martinet conjectures for the distributions of class groups of number fields, and further the understanding of their implications. We start by giving a simpler statement of the conjectures. We show that the probabilities that arise are inversely proportional the to number of automorphisms of structures slightly larger than the class groups. We find the moments of the Cohen-Lenstra-Martinet distributions and prove that the distributions are determined by their moments. In order to apply these conjectures to class groups of non-Galois fields, we prove a new theorem on the capitulation kernel (of ideal classes that become trivial in a larger field) to relate the class groups of non-Galois fields to the class groups of Galois fields. We then construct an integral model of the Hecke algebra of a finite group, show that it acts naturally on class groups of non-Galois fields, and prove that the Cohen-Lenstra-Martinet conjectures predict a distribution for class groups of non-Galois fields that involves the inverse of the number of automorphisms of the class group as a Hecke-module.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44999061","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 20
The Euler characteristic of Out($F_n$) Out($F_n$)的欧拉特性
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2019-07-08 DOI: 10.4171/CMH/501
M. Borinsky, K. Vogtmann
{"title":"The Euler characteristic of Out($F_n$)","authors":"M. Borinsky, K. Vogtmann","doi":"10.4171/CMH/501","DOIUrl":"https://doi.org/10.4171/CMH/501","url":null,"abstract":". We prove that the rational Euler characteristic of Out( F n ) is always negative and its asymptotic growth rate is Γ( n − 32 ) / √ 2 π log 2 n . This settles a 1987 conjecture of J. Smillie and the second author. We establish connections with the Lambert W -function and the zeta function.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42865182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 12
Free rational points on smooth hypersurfaces 光滑超曲面上的自由有理点
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2019-06-20 DOI: 10.4171/cmh/499
T. Browning, W. Sawin
{"title":"Free rational points on smooth hypersurfaces","authors":"T. Browning, W. Sawin","doi":"10.4171/cmh/499","DOIUrl":"https://doi.org/10.4171/cmh/499","url":null,"abstract":"Motivated by a recent question of Peyre, we apply the Hardy-Littlewood circle method to count \"sufficiently free\" rational points of bounded height on arbitrary smooth projective hypersurfaces of low degree that are defined over the rational numbers.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/cmh/499","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49537188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Rigidity of center Lyapunov exponents and $su$-integrability 中心Lyapunov指数的刚性与$su$-可积性
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2019-05-20 DOI: 10.4171/cmh/497
Shaobo Gan, Yi Shi
{"title":"Rigidity of center Lyapunov exponents and $su$-integrability","authors":"Shaobo Gan, Yi Shi","doi":"10.4171/cmh/497","DOIUrl":"https://doi.org/10.4171/cmh/497","url":null,"abstract":"Let $f$ be a conservative partially hyperbolic diffeomorphism, which is homotopic to an Anosov automorphism $A$ on $mathbb{T}^3$. We show that the stable and unstable bundles of $f$ are jointly integrable if and only if every periodic point of $f$ admits the same center Lyapunov exponent with $A$. In particular, $f$ is Anosov. Thus every conservative partially hyperbolic diffeomorphism, which is homotopic to an Anosov automorphism on $mathbb{T}^3$, is ergodic. This proves the Ergodic Conjecture proposed by Hertz-Hertz-Ures on $mathbb{T}^3$.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/cmh/497","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48173033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 13
$p$-adic equidistribution of CM points CM点的$p$adic等分布
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2019-04-16 DOI: 10.4171/CMH/541
Daniel Disegni
{"title":"$p$-adic equidistribution of CM points","authors":"Daniel Disegni","doi":"10.4171/CMH/541","DOIUrl":"https://doi.org/10.4171/CMH/541","url":null,"abstract":"Let $X$ be a modular curve and consider a sequence of Galois orbits of CM points in $X$, whose $p$-conductors tend to infinity. Its equidistribution properties in $X({bf C})$ and in the reductions of $X$ modulo primes different from $p$ are well understood. \u0000We study the equidistribution problem in the Berkovich analytification $X_{p}^{rm an}$ of $X_{{bf Q}_{p}}$. \u0000We partition the set of CM points of sufficiently high conductor in $X_{{bf Q}_{p}}$ into finitely many emph{basins} $B_{V}$, indexed by the irreducible components $V $ of the mod-$p$ reduction of the canonical model of $X$. We prove that a sequence $z_{n}$ of local Galois orbits of CM points with $p$-conductor going to infinity has a limit in $X_{p}^{rm an}$ if and only if it is eventually supported in a single basin $B_{V}$. If so, the limit is the unique point of $X_{p}^{rm an}$ whose mod-$p$ reduction is the generic point of $V$. \u0000The result is proved in the more general setting of Shimura curves over totally real fields. The proof combines Gross's theory of quasicanonical liftings with a new formula for the intersection numbers of CM curves and vertical components in a Lubin--Tate space.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49190302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Hyperbolic surfaces with sublinearly many systoles that fill 具有次线性多个收缩的双曲面
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2019-04-03 DOI: 10.4171/cmh/495
Maxime Fortier Bourque
{"title":"Hyperbolic surfaces with sublinearly many systoles that fill","authors":"Maxime Fortier Bourque","doi":"10.4171/cmh/495","DOIUrl":"https://doi.org/10.4171/cmh/495","url":null,"abstract":"For any e>0, we construct a closed hyperbolic surface of genus g=g(e) with a set of at most eg systoles that fill, meaning that each component of the complement of their union is contractible. This surface is also a critical point of index at most eg for the systole function, disproving the lower bound of 2g−1 conjectured by Schmutz Schaller.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/cmh/495","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41986938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Involutions and Chern numbers of varieties 品种的对合和陈氏数
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2019-03-18 DOI: 10.4171/CMH/504
Olivier Haution
{"title":"Involutions and Chern numbers of varieties","authors":"Olivier Haution","doi":"10.4171/CMH/504","DOIUrl":"https://doi.org/10.4171/CMH/504","url":null,"abstract":"Consider an involution of a smooth projective variety over a field of characteristic not two. We look at the relations between the variety and the fixed locus of the involution from the point of view of cobordism. We show in particular that the fixed locus has dimension larger than its codimension when certain Chern numbers of the variety are not divisible by two, or four. Some of those results, but not all, are analogues of theorems in algebraic topology obtained by Conner-Floyd and Boardman in the sixties. We include versions of our results concerning the vanishing loci of idempotent global derivations in characteristic two. Our approach to cobordism, following Merkurjev's, is elementary, in the sense that it does not involve resolution of singularities or homotopical methods.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41726112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
The action spectrum characterizes closed contact 3-manifolds all of whose Reeb orbits are closed 作用谱表征了闭合接触3流形，它们的Reeb轨道都是闭合的
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2019-01-29 DOI: 10.4171/CMH/493
Daniel Cristofaro-Gardiner, M. Mazzucchelli
{"title":"The action spectrum characterizes closed contact 3-manifolds all of whose Reeb orbits are closed","authors":"Daniel Cristofaro-Gardiner, M. Mazzucchelli","doi":"10.4171/CMH/493","DOIUrl":"https://doi.org/10.4171/CMH/493","url":null,"abstract":"A classical theorem due to Wadsley implies that, on a connected contact manifold all of whose Reeb orbits are closed, there is a common period for the Reeb orbits. In this paper we show that, for any Reeb flow on a closed connected 3-manifold, the following conditions are actually equivalent: (1) every Reeb orbit is closed; (2) all closed Reeb orbits have a common period; (3) the action spectrum has rank 1. We also show that, on a fixed closed connected 3-manifold, a contact form with an action spectrum of rank 1 is determined (up to pull-back by diffeomorphisms) by the set of minimal periods of its closed Reeb orbits.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/CMH/493","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47887032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 15
Cutoff on Ramanujan complexes and classical groups Ramanujan复合体和经典群的截断
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2019-01-27 DOI: 10.4171/CMH/537
Michael Chapman, Ori Parzanchevski
{"title":"Cutoff on Ramanujan complexes and classical groups","authors":"Michael Chapman, Ori Parzanchevski","doi":"10.4171/CMH/537","DOIUrl":"https://doi.org/10.4171/CMH/537","url":null,"abstract":"The total-variation cutoff phenomenon has been conjectured to hold for simple random walk on all transitive expanders. However, very little is actually known regarding this conjecture, and cutoff on sparse graphs in general. In this paper we establish total-variation cutoff for simple random walk on Ramanujan complexes of type $tilde{A}_{d}$ ($dgeq1$). As a result, we obtain explicit generators for the finite classical groups $PGL_{n}(mathbb{F}_{q})$ for which the associated Cayley graphs exhibit total-variation cutoff.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44347055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 4
Connected components of strata of Abelian differentials over Teichmüller space Teichmuüller空间上Abelian微分层的连通分量
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2019-01-16 DOI: 10.4171/cmh/491
Aaron Calderon
{"title":"Connected components of strata of Abelian differentials over Teichmüller space","authors":"Aaron Calderon","doi":"10.4171/cmh/491","DOIUrl":"https://doi.org/10.4171/cmh/491","url":null,"abstract":"This paper describes connected components of the strata of holomorphic abelian differentials on marked Riemann surfaces with prescribed degrees of zeros. Unlike the case for unmarked Riemann surfaces, we find there can be many connected components, distinguished by roots of the cotangent bundle of the surface. In the course of our investigation we also characterize the images of the fundamental groups of strata inside of the mapping class group. The main techniques of proof are mod r winding numbers and a mapping class group-theoretic analogue of the Euclidean algorithm.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/cmh/491","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49539097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 10
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信