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The Monodromy Map from Differential Systems to the Character Variety Is Generically Immersive 从微分系统到角色多样性的单一性映射通常是沉浸式的
2区 数学
Publications of the Research Institute for Mathematical Sciences Pub Date : 2023-11-09 DOI: 10.4171/prims/59-4-5
Indranil Biswas, Sorin Dumitrescu
{"title":"The Monodromy Map from Differential Systems to the Character Variety Is Generically Immersive","authors":"Indranil Biswas, Sorin Dumitrescu","doi":"10.4171/prims/59-4-5","DOIUrl":"https://doi.org/10.4171/prims/59-4-5","url":null,"abstract":"Let $G$ be a connected reductive affine algebraic group defined over $mathbb C$ and $mathfrak g$ its Lie algebra. We study the monodromy map from the space of $mathfrak g$-differential systems on a compact connected Riemann surface $Sigma$ of genus $g ,geq, 2$ to the character variety of $G$-representations of the fundamental group of $Sigma$. If the complex dimension of $G$ is at least three, we show that the monodromy map is an immersion at the generic point.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135191534","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: 0
Pro-$p$ Criterion of Good Reduction of Punctured Elliptic Curves 刺穿椭圆曲线良好约简的Pro- p准则
2区 数学
Publications of the Research Institute for Mathematical Sciences Pub Date : 2023-11-09 DOI: 10.4171/prims/59-4-6
Wojciech Porowski
{"title":"Pro-$p$ Criterion of Good Reduction of Punctured Elliptic Curves","authors":"Wojciech Porowski","doi":"10.4171/prims/59-4-6","DOIUrl":"https://doi.org/10.4171/prims/59-4-6","url":null,"abstract":"","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135192986","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: 0
Trace- and Improved Data-Processing Inequalities for von Neumann Algebras 冯诺依曼代数的跟踪和改进数据处理不等式
2区 数学
Publications of the Research Institute for Mathematical Sciences Pub Date : 2023-11-09 DOI: 10.4171/prims/59-4-1
Stefan Hollands
{"title":"Trace- and Improved Data-Processing Inequalities for von Neumann Algebras","authors":"Stefan Hollands","doi":"10.4171/prims/59-4-1","DOIUrl":"https://doi.org/10.4171/prims/59-4-1","url":null,"abstract":"We prove a version of the data-processing inequality for the relative entropy for general von Neumann algebras with an explicit lower bound involving the measured relative entropy. The inequality, which generalizes previous work by Sutter et al. on finite dimensional density matrices, yields a bound how well a quantum state can be recovered after it has been passed through a channel. The natural applications of our results are in quantum field theory where the von Neumann algebras are known to be of type III. Along the way we generalize various multi-trace inequalities to general von Neumann algebras.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135191524","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: 4
On Galois Action on the Inertia Stack of Moduli Spaces of Curves 曲线模空间惯性叠加上的伽罗瓦作用
2区 数学
Publications of the Research Institute for Mathematical Sciences Pub Date : 2023-11-09 DOI: 10.4171/prims/59-4-2
Benjamin Collas, Sylvain Maugeais
{"title":"On Galois Action on the Inertia Stack of Moduli Spaces of Curves","authors":"Benjamin Collas, Sylvain Maugeais","doi":"10.4171/prims/59-4-2","DOIUrl":"https://doi.org/10.4171/prims/59-4-2","url":null,"abstract":"","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135192723","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: 0
Quantum Dilogarithm Identities Arising from the Product Formula for the Universal R-Matrix of Quantum Affine Algebras 由量子仿射代数的普适r矩阵乘积公式产生的量子二对数恒等式
2区 数学
Publications of the Research Institute for Mathematical Sciences Pub Date : 2023-11-09 DOI: 10.4171/prims/59-4-4
Masaru Sugawara
{"title":"Quantum Dilogarithm Identities Arising from the Product Formula for the Universal R-Matrix of Quantum Affine Algebras","authors":"Masaru Sugawara","doi":"10.4171/prims/59-4-4","DOIUrl":"https://doi.org/10.4171/prims/59-4-4","url":null,"abstract":"","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135192973","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: 0
On Cohomology Vanishing with Polynomial Growth on Complex Manifolds with Pseudoconvex Boundary 带伪凸边界的复流形上的多项式增长消失的上同调
2区 数学
Publications of the Research Institute for Mathematical Sciences Pub Date : 2023-11-09 DOI: 10.4171/prims/59-4-3
Takeo Ohsawa
{"title":"On Cohomology Vanishing with Polynomial Growth on Complex Manifolds with Pseudoconvex Boundary","authors":"Takeo Ohsawa","doi":"10.4171/prims/59-4-3","DOIUrl":"https://doi.org/10.4171/prims/59-4-3","url":null,"abstract":"","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135192976","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: 1
Further Examples of Non-geometric Sections of Arithmetic Fundamental Groups 算术基本群的非几何截面的进一步例子
2区 数学
Publications of the Research Institute for Mathematical Sciences Pub Date : 2023-10-10 DOI: 10.4171/prims/59-3-5
Mohamed Saïdi
{"title":"Further Examples of Non-geometric Sections of Arithmetic Fundamental Groups","authors":"Mohamed Saïdi","doi":"10.4171/prims/59-3-5","DOIUrl":"https://doi.org/10.4171/prims/59-3-5","url":null,"abstract":"We show the existence of group-theoretic sections of certain geometrically pro-nilpotent by abelian arithmetic fundamental groups of hyperbolic curves over $p$-adic local fields which are non-geometric, i.e., which do not arise from rational points. Among these quotients is the geometrically metabelian arithmetic fundamental group.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136293630","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: 0
Enhanced Nearby and Vanishing Cycles in Dimension One and Fourier Transform 一维增强邻近循环和消失循环及傅里叶变换
2区 数学
Publications of the Research Institute for Mathematical Sciences Pub Date : 2023-10-10 DOI: 10.4171/prims/59-3-4
Andrea D’Agnolo, Masaki Kashiwara
{"title":"Enhanced Nearby and Vanishing Cycles in Dimension One and Fourier Transform","authors":"Andrea D’Agnolo, Masaki Kashiwara","doi":"10.4171/prims/59-3-4","DOIUrl":"https://doi.org/10.4171/prims/59-3-4","url":null,"abstract":"Enhanced ind-sheaves provide a suitable framework for the irregular Riemann–Hilbert correspondence. In this paper, we give some precision on nearby and vanishing cycles for enhanced perverse objects in dimension one. As an application, we give a topological proof of the following fact. Let $mathcal{M}$ be a holonomic algebraic $mathcal{D}$-module on the affine line, and denote by ${^{mathsf{L}}}mathcal{M}$ its Fourier–Laplace transform. For a point $a$ on the affine line, denote by $ell_a$ the corresponding linear function on the dual affine line. Then the vanishing cycles of $mathcal{M}$ at $a$ are isomorphic to the graded component of degree $ell_a$ of the Stokes filtration of ${^{mathsf{L}}}mathcal{M}$ at infinity.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136293642","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
Full Justification for the Extended Green–Naghdi System for an Uneven Bottom with/without Surface Tension 对于有/没有表面张力的不均匀底部，扩展Green-Naghdi系统的充分论证
2区 数学
Publications of the Research Institute for Mathematical Sciences Pub Date : 2023-10-10 DOI: 10.4171/prims/59-3-6
Bashar Khorbatly, Samer Israwi
{"title":"Full Justification for the Extended Green–Naghdi System for an Uneven Bottom with/without Surface Tension","authors":"Bashar Khorbatly, Samer Israwi","doi":"10.4171/prims/59-3-6","DOIUrl":"https://doi.org/10.4171/prims/59-3-6","url":null,"abstract":"This paper is a continuation of a previous work on the extended Green–Naghdi system. We prolong the system, in arbitrary dimension, with/without surface tension, and for a general bottom topography. Confining the work to the one-dimensional case, wellposedness and consistency with respect to initial data and parameters are proved, taking into account the effect of surface tension. The results are local, but long term in the sense of dependence upon initial data. As a conclusion, our solution remains close to the exact solution of the full Euler system with a better (smaller) precision and therefore the full justification of the models.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136294081","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
Formal Stationary Phase for the Mellin Transform of a $mathcal D$-Module 数学D -模的Mellin变换的形式平稳相位
2区 数学
Publications of the Research Institute for Mathematical Sciences Pub Date : 2023-10-10 DOI: 10.4171/prims/59-3-2
Ricardo García López
{"title":"Formal Stationary Phase for the Mellin Transform of a $mathcal D$-Module","authors":"Ricardo García López","doi":"10.4171/prims/59-3-2","DOIUrl":"https://doi.org/10.4171/prims/59-3-2","url":null,"abstract":"Given a holonomic $mathbb{C}[z,z^{-1}]langle partial_zrangle$-module $mathbb{M}$, following Loeser and Sabbah (Comment. Math. Helv. $mathbf{66}$ (1991), 458–503), one can consider its Mellin transform, which is a difference system on the affine line over $mathbb{C}$. In this note we prove a stationary phase formula, which shows that its formal behavior at infinity is determined by the local germs defined by $mathbb{M}$ at its singular points.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136294080","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: 0
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