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A Riemann–Hilbert correspondence in positive characteristic 正特征中的Riemann-Hilbert对应
IF 1.6 2区 数学
Cambridge Journal of Mathematics Pub Date : 2017-11-11 DOI: 10.4310/CJM.2019.V7.N1.A3
B. Bhatt, J. Lurie
{"title":"A Riemann–Hilbert correspondence in positive characteristic","authors":"B. Bhatt, J. Lurie","doi":"10.4310/CJM.2019.V7.N1.A3","DOIUrl":"https://doi.org/10.4310/CJM.2019.V7.N1.A3","url":null,"abstract":"We explain a version of the Riemann-Hilbert correspondence for $p$-torsion 'etale sheaves on an arbitrary $mathbf{F}_p$-scheme.","PeriodicalId":48573,"journal":{"name":"Cambridge Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2017-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49105284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 14
On the structure of some $p$-adic period domains 关于一些$p$进周期域的结构
IF 1.6 2区 数学
Cambridge Journal of Mathematics Pub Date : 2017-10-18 DOI: 10.4310/cjm.2021.v9.n1.a4
Miaofen Chen, Laurent Fargues, Xu Shen
{"title":"On the structure of some $p$-adic period domains","authors":"Miaofen Chen, Laurent Fargues, Xu Shen","doi":"10.4310/cjm.2021.v9.n1.a4","DOIUrl":"https://doi.org/10.4310/cjm.2021.v9.n1.a4","url":null,"abstract":"We prove the Fargues-Rapoport conjecture for p-adic period domains: for a reductive group G over a p-adic field and a minuscule cocharacter {mu} of G, the weakly admissible locus coincides with the admissible one if and only if the Kottwitz set B(G,{mu}) is fully Hodge-Newton decomposable.","PeriodicalId":48573,"journal":{"name":"Cambridge Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2017-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45364649","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 24
On tidal energy in Newtonian two-body motion 论牛顿运动中的潮汐能
IF 1.6 2区 数学
Cambridge Journal of Mathematics Pub Date : 2017-08-14 DOI: 10.4310/cjm.2019.v7.n4.a2
Shuang Miao, S. Shahshahani
{"title":"On tidal energy in Newtonian two-body motion","authors":"Shuang Miao, S. Shahshahani","doi":"10.4310/cjm.2019.v7.n4.a2","DOIUrl":"https://doi.org/10.4310/cjm.2019.v7.n4.a2","url":null,"abstract":"In this work, which is based on an essential linear analysis carried out by Christodoulou, we study the evolution of tidal energy for the motion of two gravitating incompressible fluid balls with free boundaries obeying the Euler-Poisson equations. The orbital energy is defined as the mechanical energy of the two bodies' center of mass. According to the classical analysis of Kepler and Newton, when the fluids are replaced by point masses, the conic curve describing the trajectories of the masses is a hyperbola when the orbital energy is positive and an ellipse when the orbital energy is negative. The orbital energy is conserved in the case of point masses. If the point masses are initially very far, then the orbital energy is positive, corresponding to hyperbolic motion. However, in the motion of fluid bodies the orbital energy is no longer conserved because part of the conserved energy is used in deforming the boundaries of the bodies. In this case the total energy $tilde{mathcal{E}}$ can be decomposed into a sum $tilde{mathcal{E}}:=widetilde{mathcal{E}_{{mathrm{orbital}}}}+widetilde{mathcal{E}_{{mathrm{tidal}}}}$, with $widetilde{mathcal{E}_{{mathrm{tidal}}}}$ measuring the energy used in deforming the boundaries, such that if $widetilde{mathcal{E}_{{mathrm{orbital}}}} 0$, then the orbit of the bodies must be bounded. In this work we prove that under appropriate conditions on the initial configuration of the system, the fluid boundaries and velocity remain regular up to the point of the first closest approach in the orbit, and that the tidal energy $widetilde{mathcal{E}_{{mathrm{tidal}}}}$ can be made arbitrarily large relative to the total energy $tilde{mathcal{E}}$. In particular under these conditions $widetilde{mathcal{E}_{{mathrm{orbital}}}}$, which is initially positive, becomes negative before the point of the first closest approach.","PeriodicalId":48573,"journal":{"name":"Cambridge Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2017-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44140504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
A restriction isomorphism for zero-cycles with coefficients in Milnor K-theory Milnor k理论中带系数零环的约束同构
IF 1.6 2区 数学
Cambridge Journal of Mathematics Pub Date : 2017-06-30 DOI: 10.4310/CJM.2019.V7.N1.A1
Morten Lüders
{"title":"A restriction isomorphism for zero-cycles with coefficients in Milnor K-theory","authors":"Morten Lüders","doi":"10.4310/CJM.2019.V7.N1.A1","DOIUrl":"https://doi.org/10.4310/CJM.2019.V7.N1.A1","url":null,"abstract":"We prove a restriction isomorphism for zero-cycles with coefficients in Milnor K-theory for smooth projective schemes over excellent henselian discrete valuation rings. Furthermore we relate zero-cycles with coefficients in Milnor K-theory to 'etale cohomology and certain Kato complexes and deduce finiteness results for zero-cycles with coefficients in Milnor K-theory over local fields.","PeriodicalId":48573,"journal":{"name":"Cambridge Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2017-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43325839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
On Yau’s uniformization conjecture 论丘的均匀化猜想
IF 1.6 2区 数学
Cambridge Journal of Mathematics Pub Date : 2016-06-29 DOI: 10.4310/CJM.2019.V7.N1.A2
Gang Liu
{"title":"On Yau’s uniformization conjecture","authors":"Gang Liu","doi":"10.4310/CJM.2019.V7.N1.A2","DOIUrl":"https://doi.org/10.4310/CJM.2019.V7.N1.A2","url":null,"abstract":"Let $M^n$ be a complete noncompact Kahler manifold with nonnegative bisectional curvature and maximal volume growth, we prove that $M$ is biholomorphic to $mathbb{C}^n$. This confirms Yau's uniformization conjecture when M has maximal volume growth.","PeriodicalId":48573,"journal":{"name":"Cambridge Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2016-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70404418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 21
On the analogy between real reductive groups and Cartan motion groups: the Mackey–Higson bijection 实约化群与Cartan运动群的类比:麦基-希格森双射
IF 1.6 2区 数学
Cambridge Journal of Mathematics Pub Date : 2015-10-09 DOI: 10.4310/cjm.2021.v9.n3.a1
Alexandre Afgoustidis
{"title":"On the analogy between real reductive groups and Cartan motion groups: the Mackey–Higson bijection","authors":"Alexandre Afgoustidis","doi":"10.4310/cjm.2021.v9.n3.a1","DOIUrl":"https://doi.org/10.4310/cjm.2021.v9.n3.a1","url":null,"abstract":"George Mackey suggested in 1975 that there should be analogies between the irreducible unitary representations of a noncompact reductive Lie group $G$ and those of its Cartan motion group $G_0$ $-$ the semidirect product of a maximal compact subgroup of $G$ and a vector space. He conjectured the existence of a natural one-to-one correspondence between \"most\" irreducible (tempered) representations of $G$ and \"most\" irreducible (unitary) representations of $G_0$. We here describe a simple and natural bijection between the tempered duals of both groups, and an extension to a one-to-one correspondence between the admissible duals.","PeriodicalId":48573,"journal":{"name":"Cambridge Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2015-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70404522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
$(1,1)$ forms with specified Lagrangian phase: a priori estimates and algebraic obstructions 具有特定拉格朗日相的$(1,1)$形式:先验估计和代数障碍
IF 1.6 2区 数学
Cambridge Journal of Mathematics Pub Date : 2015-08-08 DOI: 10.4310/cjm.2020.v8.n2.a4
Tristan C. Collins, Adam Jacob, S. Yau
{"title":"$(1,1)$ forms with specified Lagrangian phase: a priori estimates and algebraic obstructions","authors":"Tristan C. Collins, Adam Jacob, S. Yau","doi":"10.4310/cjm.2020.v8.n2.a4","DOIUrl":"https://doi.org/10.4310/cjm.2020.v8.n2.a4","url":null,"abstract":"Let $(X,alpha)$ be a K\"ahler manifold of dimension n, and let $[omega] in H^{1,1}(X,mathbb{R})$. We study the problem of specifying the Lagrangian phase of $omega$ with respect to $alpha$, which is described by the nonlinear elliptic equation [ sum_{i=1}^{n} arctan(lambda_i)= h(x) ] where $lambda_i$ are the eigenvalues of $omega$ with respect to $alpha$. When $h(x)$ is a topological constant, this equation corresponds to the deformed Hermitian-Yang-Mills (dHYM) equation, and is related by Mirror Symmetry to the existence of special Lagrangian submanifolds of the mirror. We introduce a notion of subsolution for this equation, and prove a priori $C^{2,beta}$ estimates when $|h|>(n-2)frac{pi}{2}$ and a subsolution exists. Using the method of continuity we show that the dHYM equation admits a smooth solution in the supercritical phase case, whenever a subsolution exists. Finally, we discover some stability-type cohomological obstructions to the existence of solutions to the dHYM equation and we conjecture that when these obstructions vanish the dHYM equation admits a solution. We confirm this conjecture for complex surfaces.","PeriodicalId":48573,"journal":{"name":"Cambridge Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2015-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70404495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 76
Homotopy invariant presheaves with framed transfers 带框架转移的同伦不变预轴
IF 1.6 2区 数学
Cambridge Journal of Mathematics Pub Date : 2015-04-03 DOI: 10.4310/cjm.2020.v8.n1.a1
G. Garkusha, I. Panin
{"title":"Homotopy invariant presheaves with framed transfers","authors":"G. Garkusha, I. Panin","doi":"10.4310/cjm.2020.v8.n1.a1","DOIUrl":"https://doi.org/10.4310/cjm.2020.v8.n1.a1","url":null,"abstract":"The category of framed correspondences $Fr_*(k)$, framed presheaves and framed sheaves were invented by Voevodsky in his unpublished notes [12]. Based on the theory, framed motives are introduced and studied in [7]. The main aim of this paper is to prove that for any $mathbb A^1$-invariant quasi-stable radditive framed presheaf of Abelian groups $mathcal F$, the associated Nisnevich sheaf $mathcal F_{nis}$ is $mathbb A^1$-invariant whenever the base field $k$ is infinite of characteristic different from 2. Moreover, if the base field $k$ is infinite perfect of characteristic different from 2, then every $mathbb A^1$-invariant quasi-stable Nisnevich framed sheaf of Abelian groups is strictly $mathbb A^1$-invariant and quasi-stable. Furthermore, the same statements are true in characteristic 2 if we also assume that the $mathbb A^1$-invariant quasi-stable radditive framed presheaf of Abelian groups $mathcal F$ is a presheaf of $mathbb Z[1/2]$-modules. This result and the paper are inspired by Voevodsky's paper [13].","PeriodicalId":48573,"journal":{"name":"Cambridge Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2015-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70404443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 39
One-sided curvature estimates for H-disks h盘的单侧曲率估计
IF 1.6 2区 数学
Cambridge Journal of Mathematics Pub Date : 2014-08-22 DOI: 10.4310/cjm.2020.v8.n3.a2
W. Meeks, G. Tinaglia
{"title":"One-sided curvature estimates for H-disks","authors":"W. Meeks, G. Tinaglia","doi":"10.4310/cjm.2020.v8.n3.a2","DOIUrl":"https://doi.org/10.4310/cjm.2020.v8.n3.a2","url":null,"abstract":"In this paper we prove an extrinsic one-sided curvature estimate for disks embedded in $mathbb{R}^3$ with constant mean curvature which is independent of the value of the constant mean curvature. We apply this extrinsic one-sided curvature estimate in [24] to prove to prove a weak chord arc type result for these disks. In Section 4 we apply this weak chord arc result to obtain an intrinsic version of the one-sided curvature estimate for disks embedded in $mathbb{R}^3$ with constant mean curvature. In a natural sense, these one-sided curvature estimates generalize respectively, the extrinsic and intrinsic one-sided curvature estimates for minimal disks embedded in $mathbb{R}^3$ given by Colding and Minicozzi in Theorem 0.2 of [8] and in Corollary 0.8 of [9].","PeriodicalId":48573,"journal":{"name":"Cambridge Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2014-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70404502","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
An infinite-dimensional phenomenon in finite-dimensional metric topology 有限维度量拓扑中的无限维现象
IF 1.6 2区 数学
Cambridge Journal of Mathematics Pub Date : 2006-10-31 DOI: 10.4310/cjm.2020.v8.n1.a2
A. Dranishnikov, S. Ferry, S. Weinberger
{"title":"An infinite-dimensional phenomenon in finite-dimensional metric topology","authors":"A. Dranishnikov, S. Ferry, S. Weinberger","doi":"10.4310/cjm.2020.v8.n1.a2","DOIUrl":"https://doi.org/10.4310/cjm.2020.v8.n1.a2","url":null,"abstract":"We show that there are homotopy equivalences $h:Nto M$ between closed manifolds which are induced by cell-like maps $p:Nto X$ and $q:Mto X$ but which are not homotopic to homeomorphisms. The phenomenon is based on construction of cell-like maps that kill certain $mathbb L$-classes. The image space in these constructions is necessarily infinite-dimensional. In dimension $>6$ we classify all such homotopy equivalences. As an application, we show that such homotopy equivalences are realized by deformations of Riemannian manifolds in Gromov-Hausdorff space preserving a contractibility function.","PeriodicalId":48573,"journal":{"name":"Cambridge Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2006-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70404449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
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