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A Note on Real Line Bundles with Connection and Real Smooth Deligne Cohomology 关于带连接的实线束和实光滑德利涅同调的说明
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-06-05 DOI: 10.1007/s40306-024-00538-4
Peter Marius Flydal, Gereon Quick, Eirik Eik Svanes
{"title":"A Note on Real Line Bundles with Connection and Real Smooth Deligne Cohomology","authors":"Peter Marius Flydal,&nbsp;Gereon Quick,&nbsp;Eirik Eik Svanes","doi":"10.1007/s40306-024-00538-4","DOIUrl":"10.1007/s40306-024-00538-4","url":null,"abstract":"<div><p>We define a Real version of smooth Deligne cohomology for manifolds with involution which interpolates between equivariant sheaf cohomology and smooth imaginary-valued forms. Our main result is a classification of Real line bundles with Real connection on manifolds with involution.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 2","pages":"187 - 199"},"PeriodicalIF":0.3,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-024-00538-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142410022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Meromorphic Solutions of a Certain Type of Nonlinear Differential Equations 某类非线性微分方程的同态解
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-05-31 DOI: 10.1007/s40306-024-00539-3
Yan-Yan Feng, Jun-Fan Chen
{"title":"Meromorphic Solutions of a Certain Type of Nonlinear Differential Equations","authors":"Yan-Yan Feng,&nbsp;Jun-Fan Chen","doi":"10.1007/s40306-024-00539-3","DOIUrl":"10.1007/s40306-024-00539-3","url":null,"abstract":"<div><p>In this paper, using Nevanlinna theory and linear algebra, we characterize transcendental meromorphic solutions of nonlinear differential equation of the form </p><div><div><span>$$begin{aligned} f^n+Q_d(z,f)=sum _{i=1}^{l}p_{i}(z)e^{alpha _{i}(z)}, end{aligned}$$</span></div></div><p>where <span>(lge 2)</span>, <span>(nge l+2)</span> are integers, <i>f</i>(<i>z</i>) is a meromorphic function, <span>(Q_d(z,f))</span> is a differential polynomial in <i>f</i>(<i>z</i>) of degree <span>(dle n-(l+1))</span> with rational functions as its coefficients, <span>(p_{1}(z))</span>, <span>(p_{2}(z))</span>, <span>(dots )</span>, <span>(p_{l}(z))</span> are non-vanishing rational functions and <span>(alpha _{1}(z))</span>, <span>(alpha _{2}(z))</span>, <span>(dots )</span>, <span>(alpha _{l}(z))</span> are nonconstant polynomials such that <span>(alpha _{1}^prime (z))</span>, <span>(alpha _{2}^prime (z))</span>, <span>(dots )</span>, <span>(alpha _{l}^prime (z))</span> are distinct. Further, we give the necessary conditions for the existence of meromorphic solutions of the above equation, and supply the example to demonstrate the sharpness of the condition of the obtained theorem.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 2","pages":"173 - 186"},"PeriodicalIF":0.3,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142415235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Tight Closure, Coherence, and Localization at Single Elements 单元素的紧密闭合、相干和定位
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-05-24 DOI: 10.1007/s40306-024-00533-9
Neil Epstein
{"title":"Tight Closure, Coherence, and Localization at Single Elements","authors":"Neil Epstein","doi":"10.1007/s40306-024-00533-9","DOIUrl":"10.1007/s40306-024-00533-9","url":null,"abstract":"<div><p>In this note, a condition (<i>open persistence</i>) is presented under which a (pre)closure operation on submodules (resp. ideals) over rings of global sections over a scheme <i>X</i> can be extended to a (pre)closure operation on sheaves of submodules of a coherent <span>(mathcal {O}_X)</span>-module (resp. sheaves of ideals in <span>(mathcal {O}_X)</span>). A second condition (<i>glueability</i>) is given for such an operation to behave nicely. It is shown that for an operation that satisfies both conditions, the question of whether the operation commutes with localization at single elements is equivalent to the question of whether the new operation preserves quasi-coherence. It is shown that both conditions hold for tight closure and some of its important variants, thus yielding a geometric reframing of the open question of whether tight closure localizes at single elements. A new singularity type (<i>semi F-regularity</i>) arises, which sits between F-regularity and weak F-regularity. The paper ends with (1) a case where semi F-regularity and weak F-regularity coincide, and (2) a case where they cannot coincide without implying a solution to a major conjecture.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 2","pages":"201 - 215"},"PeriodicalIF":0.3,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-024-00533-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413482","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Topological Representation Theory from Quivers 从Quivers论拓扑表示理论
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-05-21 DOI: 10.1007/s40306-024-00531-x
Fang Li, Zhihao Wang, Jie Wu, Bin Yu
{"title":"On Topological Representation Theory from Quivers","authors":"Fang Li,&nbsp;Zhihao Wang,&nbsp;Jie Wu,&nbsp;Bin Yu","doi":"10.1007/s40306-024-00531-x","DOIUrl":"10.1007/s40306-024-00531-x","url":null,"abstract":"<div><p>In this work, we introduce <i>topological representations of a quiver</i> as a system consisting of topological spaces and its relationships determined by the quiver. Such a setting gives a natural connection between topological representations of a quiver and diagrams of topological spaces. Firstly, we investigate the relation between the category of topological representations and that of linear representations of a quiver via <span>(P(varGamma ))</span>-<span>(mathcal {TOP}^o)</span> and <span>(kvarGamma )</span>-Mod, concerning (positively) graded or vertex (positively) graded modules. Secondly, we discuss the homological theory of topological representations of quivers via the <span>(varGamma )</span>-limit functor <span>(lim ^{varGamma })</span>, and use it to define the homology groups of topological representations of quivers via <span>(H _n)</span>. It is found that some properties of a quiver can be read from homology groups. Thirdly, we investigate the homotopy theory of topological representations of quivers. We define the homotopy equivalence between two morphisms in <span>({textbf {Top}}text{- }{} {textbf {Rep}}varGamma )</span> and show that the parallel Homotopy Axiom also holds for top-representations based on the homotopy equivalence. Last, we obtain the functor <span>(At^{varGamma })</span> from <span>({textbf {Top}}text{- }{} {textbf {Rep}}varGamma )</span> to <span>({textbf {Top}})</span> and show that <span>(At^{varGamma })</span> preserves homotopy equivalence between morphisms. The relationship between the homotopy groups of a top-representation (<i>T</i>, <i>f</i>) and the homotopy groups of <span>(At^{varGamma }(T,f))</span> is also established.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 4","pages":"563 - 594"},"PeriodicalIF":0.3,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142761893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Products of Commutators of Involutions in Skew Linear Groups 斜线性群中卷积的换元积
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-05-09 DOI: 10.1007/s40306-024-00532-w
Nguyen Thi Thai Ha, Phan Hoang Nam, Tran Nam Son
{"title":"Products of Commutators of Involutions in Skew Linear Groups","authors":"Nguyen Thi Thai Ha,&nbsp;Phan Hoang Nam,&nbsp;Tran Nam Son","doi":"10.1007/s40306-024-00532-w","DOIUrl":"10.1007/s40306-024-00532-w","url":null,"abstract":"<div><p>In connection with [Theorem 4.6, Linear Algebra Appl. <b>646</b>, 119–131, (2022)], we show that each matrix in the commutator subgroup of the general linear group over a centrally-finite division ring <i>D</i>, in which each element in the commutator subgroup of <i>D</i> is a product of at most <i>s</i> commutators, can be written as a product of at most <span>(3+3leftlceil frac{s}{lfloor n/2 rfloor } rightrceil )</span> commutators of involutions if <span>(mathrm {char,}Dne 2)</span>, where <span>({displaystyle lceil x rceil })</span>, <span>({displaystyle lfloor x rfloor })</span> denote the ceiling and floor functions of <i>x</i>, respectively. Moreover, we also present the special case when <span>(D= mathbb {H})</span>, the division ring of quaternions, and an application in real group algebras.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 2","pages":"253 - 263"},"PeriodicalIF":0.3,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140994344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Schmidt’s Subspace Theorem for Moving Hyperplane Targets Over Function Fields 函数场上移动超平面目标的施密特子空间定理
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-05-07 DOI: 10.1007/s40306-024-00529-5
Le Giang, Tran Van Tan, Nguyen Van Thin
{"title":"A Schmidt’s Subspace Theorem for Moving Hyperplane Targets Over Function Fields","authors":"Le Giang,&nbsp;Tran Van Tan,&nbsp;Nguyen Van Thin","doi":"10.1007/s40306-024-00529-5","DOIUrl":"10.1007/s40306-024-00529-5","url":null,"abstract":"<div><p>The Schmidt subspace theorem has been studied extensively for both cases of fixed and moving targets in projective spaces over number fields and the case of fixed targets in projective spaces over function fields. This paper studies the case of function fields with moving targets; in particular, we extend the result of Min Ru and Paul Vojta in the Inventiones Mathematicae (1997) to the case of moving hyperplane targets in projective spaces over function fields.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 2","pages":"241 - 251"},"PeriodicalIF":0.3,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141002436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sparse-grid Sampling Recovery and Numerical Integration of Functions Having Mixed Smoothness 具有混合平滑性的函数的稀疏网格采样恢复和数值积分
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-04-23 DOI: 10.1007/s40306-024-00527-7
Dinh Dũng
{"title":"Sparse-grid Sampling Recovery and Numerical Integration of Functions Having Mixed Smoothness","authors":"Dinh Dũng","doi":"10.1007/s40306-024-00527-7","DOIUrl":"10.1007/s40306-024-00527-7","url":null,"abstract":"<div><p>We give a short survey of recent results on sparse-grid linear algorithms of approximate recovery and integration of functions possessing a unweighted or weighted Sobolev mixed smoothness based on their sampled values at a certain finite set. Some of them are extended to more general cases.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 3","pages":"377 - 426"},"PeriodicalIF":0.3,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714305","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Uniform Symbolic Topologies and Hypersurfaces 统一符号拓扑和超曲面
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-03-26 DOI: 10.1007/s40306-024-00526-8
Craig Huneke, Daniel Katz
{"title":"Uniform Symbolic Topologies and Hypersurfaces","authors":"Craig Huneke,&nbsp;Daniel Katz","doi":"10.1007/s40306-024-00526-8","DOIUrl":"10.1007/s40306-024-00526-8","url":null,"abstract":"<div><p>We study the question of which rings, and which families of ideals, have uniform symbolic topologies. In particular, we show that the uniform symbolic topology property holds for all dimension one primes in any normal complete local domain, provided dimension one primes in hypersurfaces have the uniform symbolic topology property. We also discuss bootstrapping techniques and provide a strong bootstrapping statement in positive characteristic. We apply these techniques to give families of primes in hypersurfaces of positive characteristic which have uniform symbolic topologies.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 1","pages":"99 - 113"},"PeriodicalIF":0.3,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-024-00526-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140378297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Nilpotent-invariant One-sided Ideals 论无穷不变的单边理想
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-03-16 DOI: 10.1007/s40306-024-00524-w
Truong Cong Quynh, Truong Thi Thuy Van
{"title":"On Nilpotent-invariant One-sided Ideals","authors":"Truong Cong Quynh,&nbsp;Truong Thi Thuy Van","doi":"10.1007/s40306-024-00524-w","DOIUrl":"10.1007/s40306-024-00524-w","url":null,"abstract":"<div><p>The notion of a nilpotent-invariant module was introduced and thoroughly investigated in Koşan and Quynh (Comm. Algebra <b>45</b>, 2775–2782 2017) as a proper extension of an automorphism-invariant module. In this paper a ring is called a right <span>(mathfrak {n})</span>-ring if every right ideal is nilpotent-invariant. We show that a right <span>(mathfrak {n})</span>-ring is the direct sum of a square full semisimple artinian ring and a right square-free ring. Moreover, right <span>(mathfrak {n})</span>-rings are shown to be stably finite, and if the ring is also an exchange ring then it satisfies the substitution property, has stable range 1. These results are non-trivial extensions of similar ones on rings every right ideal is automorphism-invariant.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 1","pages":"115 - 128"},"PeriodicalIF":0.3,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140236097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bounds for the Hilbert-Kunz Multiplicity of Singular Rings 奇异环的希尔伯特-昆兹乘数界限
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-03-04 DOI: 10.1007/s40306-024-00525-9
Nicholas O. Cox-Steib, Ian M. Aberbach
{"title":"Bounds for the Hilbert-Kunz Multiplicity of Singular Rings","authors":"Nicholas O. Cox-Steib,&nbsp;Ian M. Aberbach","doi":"10.1007/s40306-024-00525-9","DOIUrl":"10.1007/s40306-024-00525-9","url":null,"abstract":"<div><p>In this paper, we prove that the Watanabe-Yoshida conjecture holds up to dimension 7. Our primary new tool is a function, <span>(varphi _J(R;z^t),)</span> that interpolates between the Hilbert-Kunz multiplicities of a base ring, <i>R</i>, and various radical extensions, <span>(R_n)</span>. We prove that this function is concave and show that its rate of growth is related to the size of <span>(e_{textrm{HK}}(R))</span>. We combine techniques from Celikbas et al. (Nagoya Math. J. <b>205</b>, 149–165, 2012) and Aberbach and Enescu (Nagoya Math. J. <b>212</b>, 59–85, 2013) to get effective lower bounds for <span>(varphi ,)</span> which translate to improved bounds on the size of Hilbert-Kunz multiplicities of singular rings. The improved inequalities are powerful enough to show that the conjecture of Watanabe and Yoshida holds in dimension 7.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 1","pages":"39 - 60"},"PeriodicalIF":0.3,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140460246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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