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The monodromy pairing for logarithmic1-motifs 对数1-基元的单配对
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2019-12-09 DOI: 10.2140/tunis.2022.4.587
Jonathan Wise
{"title":"The monodromy pairing for logarithmic\u00001-motifs","authors":"Jonathan Wise","doi":"10.2140/tunis.2022.4.587","DOIUrl":"https://doi.org/10.2140/tunis.2022.4.587","url":null,"abstract":"We describe a 3-step filtration on all logarithmic abelian varieties with constant degeneration. The obstruction to descending this filtration, as a variegated extension, from logarithmic geometry to algebraic geometry is encoded in a bilinear pairing valued in the characteristic monoid of the base. This pairing is realized as the monodromy pairing in p-adic, l-adic, and Betti cohomolgies, and recovers the Picard-Lefschetz transformation in the case of Jacobians. The Hodge realization of the filtration is the monodromy weight filtration on the limit mixed Hodge structure.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41266667","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
Square root p-adic L-functions, I : Constructionof a one-variable measure 平方根p进l函数，I:单变量测度的构造
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2019-11-05 DOI: 10.2140/tunis.2021.3.657
M. Harris
{"title":"Square root p-adic L-functions, I : Construction\u0000of a one-variable measure","authors":"M. Harris","doi":"10.2140/tunis.2021.3.657","DOIUrl":"https://doi.org/10.2140/tunis.2021.3.657","url":null,"abstract":"The Ichino-Ikeda conjecture, and its generalization to unitary groups by N. Harris, has given explicit formulas for central critical values of a large class of Rankin-Selberg tensor products. Although the conjecture is not proved in full generality, there has been considerable progress, especially for $L$-values of the form $L(1/2,BC(pi) times BC(pi'))$, where $pi$ and $pi'$ are cohomological automorphic representations of unitary groups $U(V)$ and $U(V')$, respectively. Here $V$ and $V'$ are hermitian spaces over a CM field, $V$ of dimension $n$, $V'$ of codimension $1$ in $V$, and $BC$ denotes the twisted base change to $GL(n) times GL(n-1)$. \u0000This paper contains the first steps toward generalizing the construction of my paper with Tilouine on triple product $L$-functions to this situation. We assume $pi$ is a holomorphic representation and $pi'$ varies in an ordinary Hida family (of antiholomorphic forms). The construction of the measure attached to $pi$ uses recent work of Eischen, Fintzen, Mantovan, and Varma.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44143485","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: 1
A simple proof of the Hardy inequality on Carnot groups and for some hypoelliptic families of vector fields 卡诺群上Hardy不等式的一个简单证明和一些次椭圆向量场族的证明
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2019-08-19 DOI: 10.2140/tunis.2020.2.851
Franccois Vigneron
{"title":"A simple proof of the Hardy inequality on Carnot groups and for some hypoelliptic families of vector fields","authors":"Franccois Vigneron","doi":"10.2140/tunis.2020.2.851","DOIUrl":"https://doi.org/10.2140/tunis.2020.2.851","url":null,"abstract":"We give an elementary proof of the classical Hardy inequality on any Carnot group, using only integration by parts and a fine analysis of the commutator structure, which was not deemed possible until now. We also discuss the conditions under which this technique can be generalized to deal with hypoelliptic families of vector fields, which, in this case, leads to an open problem regarding the symbol properties of the gauge norm.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/tunis.2020.2.851","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41894538","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: 1
Homotopy theory of equivariant operads with fixed colors 固定颜色等变算子的同伦理论
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2019-08-15 DOI: 10.2140/tunis.2022.4.87
P. Bonventre, L. Pereira
{"title":"Homotopy theory of equivariant operads with fixed colors","authors":"P. Bonventre, L. Pereira","doi":"10.2140/tunis.2022.4.87","DOIUrl":"https://doi.org/10.2140/tunis.2022.4.87","url":null,"abstract":"We build model structures on the category of equivariant simplicial operads with a fixed set of colors, with weak equivalences determined by families of subgroups. In particular, by specifying to the family of graph subgroups (or, more generally, one of the indexing systems of Blumberg-Hill), we obtain model structures on the category of equivariant simplicial operads with a fixed set of colors, with weak equivalences are determined by norm map data.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43481495","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: 2
Limit theorems for Jacobi ensembles with large parameters 大参数Jacobi系综的极限定理
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2019-05-20 DOI: 10.2140/tunis.2021.3.843
K. Hermann, M. Voit
{"title":"Limit theorems for Jacobi ensembles with large parameters","authors":"K. Hermann, M. Voit","doi":"10.2140/tunis.2021.3.843","DOIUrl":"https://doi.org/10.2140/tunis.2021.3.843","url":null,"abstract":"Consider Jacobi random matrix ensembles with the distributions $$c_{k_1,k_2,k_3}prod_{1leq i -1leq x_1le ...le x_Nleq 1}.$$ For $(k_1,k_2,k_3)=kappacdot (a,b,1)$ with $a,b>0$ fixed, we derive a central limit theorem for the distributions above for $kappatoinfty$. The drift and the inverse of the limit covariance matrix are expressed in terms of the zeros of classical Jacobi polynomials. We also rewrite the CLT in trigonometric form and determine the eigenvalues and eigenvectors of the limit covariance matrices. These results are related to corresponding limits for $beta$-Hermite and $beta$-Laguerre ensembles for $betatoinfty$ by Dumitriu and Edelman and by Voit.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46610018","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: 8
Symplectic geometry of p-adic Teichmülleruniformization for ordinary nilpotent indigenous bundles 普通幂零原生束p进teichm<e:1>均匀化的辛几何
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2019-05-08 DOI: 10.2140/tunis.2022.4.203
Y. Wakabayashi
{"title":"Symplectic geometry of p-adic Teichmüller\u0000uniformization for ordinary nilpotent indigenous bundles","authors":"Y. Wakabayashi","doi":"10.2140/tunis.2022.4.203","DOIUrl":"https://doi.org/10.2140/tunis.2022.4.203","url":null,"abstract":"The aim of the present paper is to provide a new aspect of the $p$-adic Teichmuller theory established by S. Mochizuki. We study the symplectic geometry of the $p$-adic formal stacks $widehat{mathcal{M}}_{g, mathbb{Z}_p}$ (= the moduli classifying $p$-adic formal curves of fixed genus $g>1$) and $widehat{mathcal{S}}_{g, mathbb{Z}_p}$ (= the moduli classifying $p$-adic formal curves of genus $g$ equipped with an indigenous bundle). A major achievement in the (classical) $p$-adic Teichmuller theory is the construction of the locus $widehat{mathcal{N}}_{g, mathbb{Z}_p}^{mathrm{ord}}$ in $widehat{mathcal{S}}_{g, mathbb{Z}_p}$ classifying $p$-adic canonical liftings of ordinary nilpotent indigenous bundles. The formal stack $widehat{mathcal{N}}_{g, mathbb{Z}_p}^{mathrm{ord}}$ embodies a $p$-adic analogue of uniformization of hyperbolic Riemann surfaces, as well as a hyperbolic analogue of Serre-Tate theory of ordinary abelian varieties. In the present paper, the canonical symplectic structure on the cotangent bundle $T^vee_{mathbb{Z}_p} widehat{mathcal{M}}_{g, mathbb{Z}_p}$ of $widehat{mathcal{M}}_{g, mathbb{Z}_p}$ is compared to Goldman's symplectic structure defined on $widehat{mathcal{S}}_{g, mathbb{Z}_p}$ after base-change by the projection $widehat{mathcal{N}}_{g, mathbb{Z}_p}^{mathrm{ord}} rightarrow widehat{mathcal{M}}_{g, mathbb{Z}_p}$. We can think of this comparison as a $p$-adic analogue of certain results in the theory of projective structures on Riemann surfaces proved by S. Kawai and other mathematicians.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44026996","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: 1
On the irreducibility of some induced representations of real reductive Lie groups 实约李群的一些诱导表示的不可约性
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2019-01-01 DOI: 10.2140/TUNIS.2019.1.73
W. Gan, Atsushi Ichino
{"title":"On the irreducibility of some induced representations of real reductive Lie groups","authors":"W. Gan, Atsushi Ichino","doi":"10.2140/TUNIS.2019.1.73","DOIUrl":"https://doi.org/10.2140/TUNIS.2019.1.73","url":null,"abstract":"","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/TUNIS.2019.1.73","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49219077","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: 4
Welcome to the Tunisian Journal of Mathematics 欢迎来到突尼斯数学杂志
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2019-01-01 DOI: 10.2140/TUNIS.2019.1.1
A. Abbes, A. Baklouti
{"title":"Welcome to the Tunisian Journal of Mathematics","authors":"A. Abbes, A. Baklouti","doi":"10.2140/TUNIS.2019.1.1","DOIUrl":"https://doi.org/10.2140/TUNIS.2019.1.1","url":null,"abstract":"","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/TUNIS.2019.1.1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68571112","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
Local estimates for Hörmander’s operatorswith Gevrey coefficients and application to the regularity of their Gevreyvectors 具有Gevrey系数的Hörmander算子的局部估计及其Gevrey向量正则性的应用
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2019-01-01 DOI: 10.2140/TUNIS.2019.1.321
M. Derridj
{"title":"Local estimates for Hörmander’s operators\u0000with Gevrey coefficients and application to the regularity of their Gevrey\u0000vectors","authors":"M. Derridj","doi":"10.2140/TUNIS.2019.1.321","DOIUrl":"https://doi.org/10.2140/TUNIS.2019.1.321","url":null,"abstract":"","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/TUNIS.2019.1.321","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68571572","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: 6
Geometric origin and some properties of the arctangential heat equation 切向热方程的几何起源和一些性质
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2019-01-01 DOI: 10.2140/TUNIS.2019.1.561
Y. Brenier
{"title":"Geometric origin and some properties of the arctangential heat equation","authors":"Y. Brenier","doi":"10.2140/TUNIS.2019.1.561","DOIUrl":"https://doi.org/10.2140/TUNIS.2019.1.561","url":null,"abstract":"We establish the geometric origin ot the nonlinear heat equation with arct-angential nonlinearity: ∂ t D = ∆(arctan D) by deriving it, together and in du-ality with the mean curvature flow equation, from the minimal surface equation in Minkowski space-time, through a suitable quadratic change of time. After examining various properties of the arctangential heat equation (in particular through its optimal transport interpretation a la Otto and its relationship with the Born-Infeld theory of Electromagnetism), we shortly discuss its possible use for image processing, once written in non-conservative form and properly discretized.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/TUNIS.2019.1.561","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68571716","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: 3
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