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Almost sure local well-posedness for the supercritical quintic NLS 超临界五次NLS的几乎确定局部适定性
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2016-12-16 DOI: 10.2140/tunis.2019.1.427
J. Brereton
{"title":"Almost sure local well-posedness for the supercritical quintic NLS","authors":"J. Brereton","doi":"10.2140/tunis.2019.1.427","DOIUrl":"https://doi.org/10.2140/tunis.2019.1.427","url":null,"abstract":"This paper studies the quintic nonlinear Schr\"odinger equation on $mathbb{R}^d$ with randomized initial data below the critical regularity $H^{frac{d-1}{2}}$. The main result is a proof of almost sure local well-posedness given a Wiener Randomization of the data in $H^s$ for $s in (frac{d-2}{2}, frac{d-1}{2})$. The argument further develops the techniques introduced in the work of 'A. B'enyi, T. Oh and O. Pocovnicu on the cubic problem. The paper concludes with a condition for almost sure global well-posedness.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2016-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/tunis.2019.1.427","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68571679","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: 18
Potentially good reduction loci of Shimura varieties 志村品种潜在的优良还原位点
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2016-11-15 DOI: 10.2140/tunis.2020.2.399
N. Imai, Yoichi Mieda
{"title":"Potentially good reduction loci of Shimura varieties","authors":"N. Imai, Yoichi Mieda","doi":"10.2140/tunis.2020.2.399","DOIUrl":"https://doi.org/10.2140/tunis.2020.2.399","url":null,"abstract":"In this paper, we give a notion of the potentially good reduction locus of a Shimura variety. It consists of the points which should be related with motives having potentially good reductions in some sense. We show the existence of such locus for a Shimura variety of preabelian type. Further, we construct a partition of the adic space associated to a Shimura variety of preabelian type, which is expected to describe degenerations of motives. Using this partition, we prove that the cohomology of the potentially good reduction locus is isomorphic to the cohomology of a Shimura variety up to non-supercuspidal parts.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2016-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/tunis.2020.2.399","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68571794","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
A proof of the refined class number formula of Gross 对格罗斯改进的类数公式的证明
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2016-08-16 DOI: 10.2140/tunis.2023.5.73
M. Hirose
{"title":"A proof of the refined class number formula of Gross","authors":"M. Hirose","doi":"10.2140/tunis.2023.5.73","DOIUrl":"https://doi.org/10.2140/tunis.2023.5.73","url":null,"abstract":"In 1988, Gross proposed a conjectural congruence between Stickelberger elements and algebraic regulators, which is often referred to as the refined class number formula. In this paper, we prove this congruence.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2016-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68572037","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
Partial resolution by toroidal blow-ups 环形爆炸的部分分辨率
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2016-08-08 DOI: 10.2140/tunis.2019.1.3
J. Koll'ar
{"title":"Partial resolution by toroidal blow-ups","authors":"J. Koll'ar","doi":"10.2140/tunis.2019.1.3","DOIUrl":"https://doi.org/10.2140/tunis.2019.1.3","url":null,"abstract":"We answer a question of Keel: How much can one improve a non-toroidal ideal sheaf by a sequence of toroidal blow-ups? Version2: Corollary 5 was proved earlier by Tevelev and Ulirsch.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2016-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/tunis.2019.1.3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68571488","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: 9
Nonlinear echoes and Landau damping with insufficient regularity 非线性回波和规律性不足的朗道阻尼
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2016-05-22 DOI: 10.2140/tunis.2021.3.121
J. Bedrossian
{"title":"Nonlinear echoes and Landau damping with insufficient regularity","authors":"J. Bedrossian","doi":"10.2140/tunis.2021.3.121","DOIUrl":"https://doi.org/10.2140/tunis.2021.3.121","url":null,"abstract":"We prove that the theorem of Mouhot and Villani on Landau damping near equilibrium for the Vlasov-Poisson equations on $mathbb{T}_x times mathbb{R}_v$ cannot, in general, be extended to high Sobolev spaces in the case of gravitational interactions. This is done by showing in every Sobolev space, there exists background distributions such that one can construct arbitrarily small perturbations that exhibit arbitrarily many isolated nonlinear oscillations in the density. These oscillations are known as plasma echoes in the physics community. For the case of electrostatic interactions, we demonstrate a sequence of small background distributions and asymptotically smaller perturbations in $H^s$ which display similar nonlinear echoes. This shows that in the electrostatic case, any extension of Mouhot and Villani's theorem to Sobolev spaces would have to depend crucially on some additional non-resonance effect coming from the background -- unlike the case of Gevrey-$nu$ with $nu < 3$ regularity, for which results are uniform in the size of small backgrounds. In particular, the uniform dependence on small background distributions obtained in Mouhot and Villani's theorem in Gevrey class is false in Sobolev spaces.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2016-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/tunis.2021.3.121","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68571436","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: 37
G-symmetric monoidal categories of modulesover equivariant commutative ring spectra 等变可交换环谱上模的g对称单一性范畴
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2015-11-23 DOI: 10.2140/tunis.2020.2.237
A. Blumberg, M. Hill
{"title":"G-symmetric monoidal categories of modules\u0000over equivariant commutative ring spectra","authors":"A. Blumberg, M. Hill","doi":"10.2140/tunis.2020.2.237","DOIUrl":"https://doi.org/10.2140/tunis.2020.2.237","url":null,"abstract":"We describe the multiplicative structures that arise on categories of equivariant modules over certain equivariant commutative ring spectra. Building on our previous work on N-infinity ring spectra, we construct categories of equivariant operadic modules over N-infinity rings that are structured by equivariant linear isometries operads. These categories of modules are endowed with equivariant symmetric monoidal structures, which amounts to the structure of an \"incomplete Mackey functor in homotopical categories\". In particular, we construct internal norms which satisfy the double coset formula. We regard the work of this paper as a first step towards equivariant derived algebraic geometry.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2015-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/tunis.2020.2.237","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68571773","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: 19
Spectral Mackey functors and equivariantalgebraic K-theory, II 谱Mackey函子与等变代数k理论，2
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2015-05-12 DOI: 10.2140/tunis.2020.2.97
C. Barwick, Saul Glasman, J. Shah
{"title":"Spectral Mackey functors and equivariant\u0000algebraic K-theory, II","authors":"C. Barwick, Saul Glasman, J. Shah","doi":"10.2140/tunis.2020.2.97","DOIUrl":"https://doi.org/10.2140/tunis.2020.2.97","url":null,"abstract":"We study the \"higher algebra\" of spectral Mackey functors, which the first named author introduced in Part I of this paper. In particular, armed with our new theory of symmetric promonoidal $infty$-categories and a suitable generalization of the second named author's Day convolution, we endow the $infty$-category of Mackey functors with a well-behaved symmetric monoidal structure. This makes it possible to speak of spectral Green functors for any operad $O$. We also answer a question of A. Mathew, proving that the algebraic $K$-theory of group actions is lax symmetric monoidal. We also show that the algebraic $K$-theory of derived stacks provides an example. Finally, we give a very short, new proof of the equivariant Barratt-Priddy-Quillen theorem, which states that the algebraic $K$-theory of the category of finite $G$-sets is simply the $G$-equivariant sphere spectrum.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2015-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/tunis.2020.2.97","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68571803","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: 57
Truncated operads and simplicial spaces 截断的操作符和简单的空格
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2015-03-24 DOI: 10.2140/tunis.2019.1.109
M. Weiss
{"title":"Truncated operads and simplicial spaces","authors":"M. Weiss","doi":"10.2140/tunis.2019.1.109","DOIUrl":"https://doi.org/10.2140/tunis.2019.1.109","url":null,"abstract":"It was shown in a recent paper by Boavida de Brito and Weiss that a well-known construction which to a plain (=monochromatic) topological operad associates a topological category and a functor from it to the category of finite sets is homotopically fully faithful, under mild conditions on the operads. The main result here is a generalization of that statement to k-truncated plain topological operads. A k-truncated operad is a weaker version of operad where all operations have arity at most k.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2015-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/tunis.2019.1.109","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68571195","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
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