发布求助
文献互助 智能选刊 最新文献

Comptes Rendus Mathematique最新文献

筛选
英文 中文
Étude des (n+1)-tissus de courbes en dimension n n维(n+1)曲线组织的研究
4区 数学
Comptes Rendus Mathematique Pub Date : 2023-11-10 DOI: 10.5802/crmath.500
Jean-Paul Dufour, Daniel Lehmann
{"title":"Étude des (n+1)-tissus de courbes en dimension n","authors":"Jean-Paul Dufour, Daniel Lehmann","doi":"10.5802/crmath.500","DOIUrl":"https://doi.org/10.5802/crmath.500","url":null,"abstract":"For (n+1)-webs by curves in an ambiant n-dimensional manifold, we first define a generalization of the well known Blaschke curvature of the dimension two, which vanishes iff the web has the maximum possible rank which is one. But, contrary to the dimension two where all 3-webs of rank one are locally isomorphic, we prove that there are infinitely many classes of isomorphism for germs of 4-webs by curves of rank one in the dimension three: we provide a procedure for building all of them, and give examples of invariants of these classes allowing in particular to distinguish the so-called quadrilateral webs among them.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135186698","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
Criterion for surjectivity of localization in Galois cohomology of a reductive group over a number field 数域上约化群伽罗瓦上同调局部的满射判据
4区 数学
Comptes Rendus Mathematique Pub Date : 2023-11-10 DOI: 10.5802/crmath.455
Mikhail Borovoi
{"title":"Criterion for surjectivity of localization in Galois cohomology of a reductive group over a number field","authors":"Mikhail Borovoi","doi":"10.5802/crmath.455","DOIUrl":"https://doi.org/10.5802/crmath.455","url":null,"abstract":"Let G be a connected reductive group over a number field F, and let S be a set (finite or infinite) of places of F. We give a necessary and sufficient condition for the surjectivity of the localization map from H 1 (F,G) to the “direct sum” of the sets H 1 (F v ,G) where v runs over S. In the appendices, we give a new construction of the abelian Galois cohomology of a reductive group over a field of arbitrary characteristic.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135141651","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
Noncommutative tensor triangulated categories and coherent frames 非交换张量三角化范畴与相干坐标系
4区 数学
Comptes Rendus Mathematique Pub Date : 2023-11-10 DOI: 10.5802/crmath.461
Vivek Mohan Mallick, Samarpita Ray
{"title":"Noncommutative tensor triangulated categories and coherent frames","authors":"Vivek Mohan Mallick, Samarpita Ray","doi":"10.5802/crmath.461","DOIUrl":"https://doi.org/10.5802/crmath.461","url":null,"abstract":"We develop a point-free approach for constructing the Nakano–Vashaw–Yakimov–Balmer spectrum of a noncommutative tensor triangulated category under certain assumptions. In particular, we provide a conceptual way of classifying radical thick tensor ideals of a noncommutative tensor triangulated category using frame theoretic methods, recovering the universal support data in the process. We further show that there is a homeomorphism between the spectral space of radical thick tensor ideals of a noncommutative tensor triangulated category and the collection of open subsets of its spectrum in the Hochster dual topology.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135141499","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: 2
Stable determination of the nonlinear term in a quasilinear elliptic equation by boundary measurements 拟线性椭圆方程非线性项的边界测量稳定确定
4区 数学
Comptes Rendus Mathematique Pub Date : 2023-11-10 DOI: 10.5802/crmath.484
Mourad Choulli
{"title":"Stable determination of the nonlinear term in a quasilinear elliptic equation by boundary measurements","authors":"Mourad Choulli","doi":"10.5802/crmath.484","DOIUrl":"https://doi.org/10.5802/crmath.484","url":null,"abstract":"We establish a Lipschitz stability inequality for the problem of determining the nonlinear term in a quasilinear elliptic equation by boundary measurements. We give a proof based on a linearization procedure together with special solutions constructed from the fundamental solution of the linearized problem.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135141920","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
Torus quotient of the Grassmannian G n,2n G的环面商n,2n
4区 数学
Comptes Rendus Mathematique Pub Date : 2023-11-10 DOI: 10.5802/crmath.501
Arpita Nayek, Pinakinath Saha
{"title":"Torus quotient of the Grassmannian G n,2n ","authors":"Arpita Nayek, Pinakinath Saha","doi":"10.5802/crmath.501","DOIUrl":"https://doi.org/10.5802/crmath.501","url":null,"abstract":"Let G n,2n be the Grassmannian parameterizing the n-dimensional subspaces of ℂ 2n . The Picard group of G n,2n is generated by a unique ample line bundle 𝒪(1). Let T be a maximal torus of SL(2n,ℂ) which acts on G n,2n and 𝒪(1). By [10, Theorem 3.10, p. 764], 2 is the minimal integer k such that 𝒪(k) descends to the GIT quotient. In this article, we prove that the GIT quotient of G n,2n (n≥3) by T with respect to 𝒪(2)=𝒪(1) ⊗2 is not projectively normal when polarized with the descent of 𝒪(2).","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135137178","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
Stability of the Levi-Civita tensors and an Alon–Tarsi type theorem Levi-Civita张量的稳定性及一个Alon-Tarsi型定理
4区 数学
Comptes Rendus Mathematique Pub Date : 2023-10-31 DOI: 10.5802/crmath.505
Damir Yeliussizov
{"title":"Stability of the Levi-Civita tensors and an Alon–Tarsi type theorem","authors":"Damir Yeliussizov","doi":"10.5802/crmath.505","DOIUrl":"https://doi.org/10.5802/crmath.505","url":null,"abstract":"We show that the Levi-Civita tensors are semistable in the sense of Geometric Invariant Theory, which is equivalent to an analogue of the Alon–Tarsi conjecture on Latin squares. The proof uses the connection of Tao’s slice rank with semistable tensors. We also show an application to an asymptotic saturation-type version of Rota’s basis conjecture.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135870023","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
Surfaces of infinite-type are non-Hopfian 无限型曲面是非hopfian曲面
4区 数学
Comptes Rendus Mathematique Pub Date : 2023-10-31 DOI: 10.5802/crmath.504
Sumanta Das, Siddhartha Gadgil
{"title":"Surfaces of infinite-type are non-Hopfian","authors":"Sumanta Das, Siddhartha Gadgil","doi":"10.5802/crmath.504","DOIUrl":"https://doi.org/10.5802/crmath.504","url":null,"abstract":"We show that finite-type surfaces are characterized by a topological analogue of the Hopf property. Namely, an oriented surface Σ is of finite-type if and only if every proper map f:Σ→Σ of degree one is homotopic to a homeomorphism.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135870193","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 Rank-One property for free Frobenius extensions 自由Frobenius扩展的秩一性质
4区 数学
Comptes Rendus Mathematique Pub Date : 2023-10-31 DOI: 10.5802/crmath.502
Gwyn Bellamy, Ulrich Thiel
{"title":"The Rank-One property for free Frobenius extensions","authors":"Gwyn Bellamy, Ulrich Thiel","doi":"10.5802/crmath.502","DOIUrl":"https://doi.org/10.5802/crmath.502","url":null,"abstract":"A conjecture by the second author, proven by Bonnaf'e-Rouquier, says that the multiplicity matrix for baby Verma modules over the restricted rational Cherednik algebra has rank one over $mathbb{Q}$ when restricted to each block of the algebra. In this paper, we show that if $H$ is a prime algebra that is a free Frobenius extension over a regular central subalgebra $R$, and the centre of $H$ is normal Gorenstein, then each central quotient $A$ of $H$ by a maximal ideal $mathfrak{m}$ of $R$ satisfies the rank one property with respect to the Cartan matrix of $A$. Examples where the result is applicable include graded Hecke algebras, extended affine Hecke algebras, quantized enveloping algebras at roots of unity, non-commutative crepant resolutions of Gorenstein domains and 3 and 4 dimensional PI Skylanin algebras. In particular, since the multiplicity matrix for restricted rational Cherednik algebras has the rank one property if and only if its Cartan matrix does, our result provides a different proof of the original conjecture.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135870826","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 γ-support as a micro-support γ-支持作为微支持
4区 数学
Comptes Rendus Mathematique Pub Date : 2023-10-31 DOI: 10.5802/crmath.499
Tomohiro Asano, Stéphane Guillermou, Vincent Humilière, Yuichi Ike, Claude Viterbo
{"title":"The γ-support as a micro-support","authors":"Tomohiro Asano, Stéphane Guillermou, Vincent Humilière, Yuichi Ike, Claude Viterbo","doi":"10.5802/crmath.499","DOIUrl":"https://doi.org/10.5802/crmath.499","url":null,"abstract":"We prove that for any element L in the completion of the space of smooth compact exact Lagrangian submanifolds of a cotangent bundle equipped with the spectral distance, the γ-support of L coincides with the reduced micro-support of its sheaf quantization. As an application, we give a characterization of the Vichery subdifferential in terms of γ-support.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135813793","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
Shape optimization using a level set based mesh evolution method: an overview and tutorial 形状优化使用基于水平集的网格进化方法:概述和教程
4区 数学
Comptes Rendus Mathematique Pub Date : 2023-10-31 DOI: 10.5802/crmath.498
Charles Dapogny, Florian Feppon
{"title":"Shape optimization using a level set based mesh evolution method: an overview and tutorial","authors":"Charles Dapogny, Florian Feppon","doi":"10.5802/crmath.498","DOIUrl":"https://doi.org/10.5802/crmath.498","url":null,"abstract":"This article revolves around a recent numerical framework for shape and topology optimization, which features an exact mesh of the shape at each iteration of the process, while still leaving the room for an arbitrary evolution of the latter (including changes in its topology). In a nutshell, two complementary representations of the shape are combined: on the one hand, it is meshed exactly, which allows for precise mechanical calculations based on the finite element method; on the other hand, it is described implicitly, using the level set method, which makes it possible to track its evolution in a robust way. In the first part of this work, we overview the main aspects of this numerical strategy. After a brief presentation of some necessary background material – related to shape optimization and meshing, among others – we describe the numerical schemes involved, notably when it comes to the practice of the level set method, the remeshing algorithms, and the considered optimization solver. This strategy is illustrated with 2d and 3d numerical examples in various physical contexts. In the second part of this article, we propose a simple albeit efficient python-based implementation of this framework. The code is described with a fair amount of details, and it is expected that the reader can easily elaborate upon the presented examples to tackle his own problems.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135765685","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
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