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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 Q2 Mathematics Pub Date : 2016-12-16 DOI: 10.2140/tunis.2019.1.427
J. Brereton
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.
研究了$mathbb{R}^d$上随机初始数据低于临界正则性$H^{frac{d-1}{2}}$的五次非线性Schr odinger方程。主要结果是给出$H^s$中$s in (frac{d-2}{2}, frac{d-1}{2})$的数据的Wiener随机化,证明了几乎肯定的局部适定性。该论证进一步发展了A的工作中引入的技术。B 'enyi T. Oh和O. Pocovnicu关于三次问题。最后给出了几乎确定全局适定性的一个条件。
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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 Q2 Mathematics Pub Date : 2016-11-15 DOI: 10.2140/tunis.2020.2.399
N. Imai, Yoichi Mieda
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.
在本文中,我们给出了一个Shimura变量的潜在好的约化轨迹的概念。它由一些点组成,这些点应该与动机有关,在某种意义上具有潜在的良好还原。我们证明了这种基因座的存在对于一个Shimura的前abel型变种。进一步,我们构造了一个与Shimura前先验类型相关的进元空间的分区,它有望描述动机的退化。利用这一划分,我们证明了潜在好的约化轨迹的上同构与一个Shimura变种的上同构直至非超尖部。
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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 Q2 Mathematics Pub Date : 2016-08-16 DOI: 10.2140/tunis.2023.5.73
M. Hirose
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.
1988年,Gross提出了Stickelberger元与代数调节器之间的推测同余式,常被称为精炼类数公式。在本文中,我们证明了这个同余。
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引用次数: 0
Partial resolution by toroidal blow-ups 环形爆炸的部分分辨率
IF 0.9 Q2 Mathematics Pub Date : 2016-08-08 DOI: 10.2140/tunis.2019.1.3
J. Koll'ar
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.
我们回答龙骨的一个问题:多少可以改善一个非环面理想轴由一个环面爆破序列?版本2:推论5早前由Tevelev和ulrsch证明过。
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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 Q2 Mathematics Pub Date : 2016-05-22 DOI: 10.2140/tunis.2021.3.121
J. Bedrossian
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.
我们证明了$mathbb{T}_x 乘以mathbb{R}_v$上的Vlasov-Poisson方程的Mouhot和Villani关于Landau阻尼接近平衡的定理一般不能推广到引力相互作用下的高Sobolev空间。这是通过在每个Sobolev空间中,存在背景分布来实现的,这样就可以构造任意小的扰动,在密度中表现出任意多的孤立非线性振荡。这些振荡在物理学界被称为等离子体回声。对于静电相互作用的情况,我们展示了一系列小背景分布和$H^s$中渐近较小的扰动,它们显示出类似的非线性回波。这表明,在静电情况下,将Mouhot和Villani定理扩展到Sobolev空间的任何扩展都必须关键地依赖于来自背景的一些额外的非共振效应——与Gevrey的情况不同,$nu$具有$nu < 3$的规律性,其结果在小背景的大小上是一致的。特别地,在Gevrey类中Mouhot和Villani定理中得到的对小背景分布的一致依赖在Sobolev空间中是不成立的。
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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 Q2 Mathematics Pub Date : 2015-11-23 DOI: 10.2140/tunis.2020.2.237
A. Blumberg, M. Hill
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.
我们描述了在某些等变交换环谱上的等变模范畴上出现的乘法结构。基于我们之前对n -无穷环光谱的研究,我们构建了n -无穷环上由等变线性等距操作数构成的等变操作模的类别。这些模的范畴被赋予了等变对称一元结构,相当于“同局部范畴中的不完全Mackey函子”的结构。特别地,我们构造了满足双陪集公式的内模。我们认为本文的工作是迈向等变代数几何的第一步。
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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 Q2 Mathematics Pub Date : 2015-05-12 DOI: 10.2140/tunis.2020.2.97
C. Barwick, Saul Glasman, J. Shah
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.
我们研究了谱Mackey函子的“高等代数”,这是第一作者在第一部分中介绍的。特别地,利用我们的新的对称原一元$infty$ -范畴理论和对第二个命名的author's Day卷积的适当推广,我们赋予了$infty$ -范畴的麦基函子一个表现良好的对称一元结构。这使得对任何操作符$O$都可以使用谱格林函子。我们还回答了a . Mathew的一个问题,证明了群作用的代数$K$ -理论是松弛对称一元的。我们还证明了派生堆栈的代数$K$ -理论提供了一个例子。最后,我们给出了一个非常简短的、新的等变baratt - priddy - quillen定理的证明,证明了有限$G$ -集合范畴的代数$K$ -理论就是$G$ -等变球谱。
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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 Q2 Mathematics Pub Date : 2015-03-24 DOI: 10.2140/tunis.2019.1.109
M. Weiss
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.
Boavida de Brito和Weiss在最近的一篇论文中证明了一个著名的构造,在操作数的温和条件下,它将一个拓扑范畴和一个从它而来的函子与有限集合的范畴联系在一起。这里的主要结果是将该语句推广到k截断的普通拓扑操作数。k截断的operad是operad的较弱版本,其中所有操作的密度最多为k。
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引用次数: 8
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Tunisian Journal of Mathematics
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