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Tunisian Journal of Mathematics最新文献

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Purity of crystalline strata 结晶地层的纯度
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2018-01-29 DOI: 10.2140/tunis.2019.1.519
Jinghao Li, A. Vasiu
{"title":"Purity of crystalline strata","authors":"Jinghao Li, A. Vasiu","doi":"10.2140/tunis.2019.1.519","DOIUrl":"https://doi.org/10.2140/tunis.2019.1.519","url":null,"abstract":"Let $p$ be a prime. Let $ninmathbb N-{0}$. Let $mathcal C$ be an $F^n$-crystal over a locally noetherian $mathbb F_p$-scheme $S$. Let $(a,b)inmathbb N^2$. We show that the reduced locally closed subscheme of $S$ whose points are exactly those $xin S$ such that $(a,b)$ is a break point of the Newton polygon of the fiber $mathcal C_x$ of $mathcal C$ at $x$ is pure in $S$, i.e., it is an affine $S$-scheme. This result refines and reobtains previous results of de Jong--Oort, Vasiu, and Yang. As an application, we show that for all $min mathbb N$ the reduced locally closed subscheme of $S$ whose points are exactly those $xin S$ for which the $p$-rank of $mathcal C_x$ is $m$ is pure in $S$; the case $n=1$ was previously obtained by Deligne (unpublished) and the general case $nge 1$ refines and reobtains a result of Zink.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2018-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/tunis.2019.1.519","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43885858","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 nonlinear estimate of the life span of solutionsof the three dimensional Navier–Stokes equations 三维Navier-Stokes方程解寿命的非线性估计
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2018-01-23 DOI: 10.2140/tunis.2019.1.273
J. Chemin, I. Gallagher
{"title":"A nonlinear estimate of the life span of solutions\u0000of the three dimensional Navier–Stokes equations","authors":"J. Chemin, I. Gallagher","doi":"10.2140/tunis.2019.1.273","DOIUrl":"https://doi.org/10.2140/tunis.2019.1.273","url":null,"abstract":"The purpose of this article is to establish bounds from below for the life span of regular solutions to the incompressible Navier-Stokes system, which \u0000involve norms not only of the initial data, but also of nonlinear functions of the initial data. We provide examples showing that those bounds are significant improvements to the one provided by the classical fixed point argument. One of the important ingredients is the use of a scale-invariant energy estimate.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2018-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/tunis.2019.1.273","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42200442","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
Ramification groups of coverings and valuations 覆盖和估值的分支群
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2018-01-09 DOI: 10.2140/tunis.2019.1.373
Takeshi Saito
{"title":"Ramification groups of coverings and valuations","authors":"Takeshi Saito","doi":"10.2140/tunis.2019.1.373","DOIUrl":"https://doi.org/10.2140/tunis.2019.1.373","url":null,"abstract":"We give a purely scheme theoretic construction of the filtration by ramification groups of the Galois group of a covering. The valuation need not be discrete but the normalizations are required to be locally of complete intersection.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2018-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/tunis.2019.1.373","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47710803","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
On log motives 关于log动机
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2017-12-28 DOI: 10.2140/tunis.2020.2.733
Tetsushi Ito, Kazuya Kato, Chikara Nakayama, S. Usui
{"title":"On log motives","authors":"Tetsushi Ito, Kazuya Kato, Chikara Nakayama, S. Usui","doi":"10.2140/tunis.2020.2.733","DOIUrl":"https://doi.org/10.2140/tunis.2020.2.733","url":null,"abstract":"We define the categories of log motives and log mixed motives. The latter gives a new formulation for the category of mixed motives. We prove that the former is a semisimple abelian category if and only if the numerical equivalence and homological equivalence coincide, and that it is also equivalent to that the latter is a Tannakian category. We discuss various realizations, formulate Tate and Hodge conjectures, and verify them in curve case.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2017-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/tunis.2020.2.733","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48837359","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: 7
A generalization of a power-conjugacy problem in torsion-free negatively curved groups 无扭负弯曲群中幂共轭问题的推广
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2017-12-06 DOI: 10.2140/tunis.2020.2.841
Rita Gitik
{"title":"A generalization of a power-conjugacy problem in torsion-free negatively curved groups","authors":"Rita Gitik","doi":"10.2140/tunis.2020.2.841","DOIUrl":"https://doi.org/10.2140/tunis.2020.2.841","url":null,"abstract":"Let H and K be quasiconvex subgroups of a negatively curved torsion-free group G. We give an algorithm which decides whether an element of H is conjugated in G to an element of K.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2017-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/tunis.2020.2.841","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46828093","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
Generic colourful tori and inverse spectral transform for Hankel operators Hankel算子的一般彩色环面和谱逆变换
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2017-12-06 DOI: 10.2140/tunis.2019.1.347
P. Gérard, S. Grellier
{"title":"Generic colourful tori and inverse spectral transform for Hankel operators","authors":"P. Gérard, S. Grellier","doi":"10.2140/tunis.2019.1.347","DOIUrl":"https://doi.org/10.2140/tunis.2019.1.347","url":null,"abstract":"This paper explores the regularity properties of an inverse spectral transform for Hilbert--Schmidt Hankel operators on the unit disc. This spectral transform plays the role of action-angles variables for an integrable infinite dimensional Hamiltonian system -- the cubic Szeg\"o equation. We investigate the regularity of functions on the tori supporting the dynamics of this system, in connection with some wave turbulence phenomenon, discovered in a previous work and due to relative small gaps between the actions. We revisit this phenomenon by proving that generic smooth functions and a G $delta$ dense set of irregular functions do coexist on the same torus. On the other hand, we establish some uniform analytic regularity for tori corresponding to rapidly decreasing actions which satisfy some specific property ruling out the phenomenon of small gaps.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2017-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/tunis.2019.1.347","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45105064","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
From compressible to incompressible inhomogeneous flows in the case of large data 在大数据的情况下，从可压缩到不可压缩非均匀流
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2017-10-24 DOI: 10.2140/tunis.2019.1.127
R. Danchin, P. Mucha
{"title":"From compressible to incompressible inhomogeneous flows in the case of large data","authors":"R. Danchin, P. Mucha","doi":"10.2140/tunis.2019.1.127","DOIUrl":"https://doi.org/10.2140/tunis.2019.1.127","url":null,"abstract":"This paper is concerned with the mathematical derivation of the inhomoge-neous incompressible Navier-Stokes equations (INS) from the compressible Navier-Stokes equations (CNS) in the large volume viscosity limit. We first prove a result of large time existence of regular solutions for (CNS). Next, as a consequence, we establish that the solutions of (CNS) converge to those of (INS) when the volume viscosity tends to infinity. Analysis is performed in the two dimensional torus, for general initial data. In particular, we are able to handle large variations of density.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2017-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/tunis.2019.1.127","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46576824","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: 10
Nilpotence theorems via homological residue fields 同调剩余域的幂零定理
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2017-10-13 DOI: 10.2140/tunis.2020.2.359
Paul Balmer
{"title":"Nilpotence theorems via homological residue fields","authors":"Paul Balmer","doi":"10.2140/tunis.2020.2.359","DOIUrl":"https://doi.org/10.2140/tunis.2020.2.359","url":null,"abstract":"We prove nilpotence theorems in tensor-triangulated categories using suitable Gabriel quotients of the module category, and discuss examples.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2017-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/tunis.2020.2.359","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43985492","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: 15
Fronts d’onde des représentations tempéréeset de réduction unipotente pour SO(2n + 1) SO（2n+1）的单能回火和还原表示的波前
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2017-10-10 DOI: 10.2140/tunis.2020.2.43
J. Waldspurger
{"title":"Fronts d’onde des représentations tempérées\u0000et de réduction unipotente pour SO(2n + 1)","authors":"J. Waldspurger","doi":"10.2140/tunis.2020.2.43","DOIUrl":"https://doi.org/10.2140/tunis.2020.2.43","url":null,"abstract":"Let G be a special orthogonal group SO(2n+1) defined over a p-adic field F. Let $pi$ be an admissible irreducible representation of G(F) which is tempered and of unipotent reduction. We prove that $pi$ has a wave front set. In some particular cases, for instance if $pi$ is of the discrete series, we give a method to compute this wave front set.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2017-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/tunis.2020.2.43","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49297461","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
Rigid local systems and alternating groups 刚性局部系统和交替群
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2017-10-06 DOI: 10.2140/TUNIS.2019.1.295
R. Guralnick, N. M. Katz, P. Tiep
{"title":"Rigid local systems and alternating groups","authors":"R. Guralnick, N. M. Katz, P. Tiep","doi":"10.2140/TUNIS.2019.1.295","DOIUrl":"https://doi.org/10.2140/TUNIS.2019.1.295","url":null,"abstract":"In earlier work, Katz exhibited some very simple one parameter families of exponential sums which gave rigid local systems on the affine line in characteristic p whose geometric (and usually, arithmetic) monodromy groups were SL(2,q), and he exhibited other such very simple families giving SU(3,q). [Here q is a power of the characteristic p with p odd]. In this paper, we exhibit equally simple families whose geometric monodromy groups are the alternating groups Alt(2q). $. We also determine their arithmetic monodromy groups. By Raynaud's solution of the Abhyankar Conjecture, any finite simple group whose order is divisible by p will occur as the geometric monodromy group of some local system on the affine line in characteristic p; the interest here is that it occurs in our particularly simple local systems. In the earlier work of Katz, he used a theorem to Kubert to know that the monodromy groups in question were finite, then work of Gross to determine which finite groups they were. Here we do not have, at present, any direct way of showing this finiteness. Rather, the situation is more complicated and more interesting. Using some basic information about these local systems, a fundamental dichotomy is proved: The geometric monodromy group is either Alt(2q) or it is the special orthogonal group SO(2q-1). An elementary polynomial identity is used to show that the third moment is 1. This rules out the SO(2q-1) case. This roundabout method establishes the theorem. It would be interesting to find a \"direct\" proof that these local systems have integer (rather than rational) traces; this integrality is in fact equivalent to their monodromy groups being finite, Even if one had such a direct proof, it would still require serious group theory to show that their geometric monodromy groups are the alternating groups.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2017-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/TUNIS.2019.1.295","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47662995","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: 7
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