Transactions of the American Mathematical Society, Series B最新文献

英文中文

A group theoretic perspective on entanglements of division fields 分域纠缠的群论视角

Transactions of the American Mathematical Society, Series B

Pub Date : 2020-08-22 DOI: 10.1090/btran/95

Harris B. Daniels, J. Morrow

In this paper, we initiate a systematic study of entanglements of division fields from a group theoretic perspective. For a positive integer n n and a subgroup G ⊆ G L 2 ( Z / n Z ) Gsubseteq GL_2( mathbb {Z}/nmathbb {Z}) with surjective determinant, we provide a definition for G G to represent an ( a , b ) (a,b) -entanglement and give additional criteria for G G to represent an explained or unexplained ( a , b

本文从群论的角度对分域的纠缠进行了系统的研究。对于正整数n n和具有满射行列式的子群G≤g2 (Z /n Z) Gsubseteq GL_2(mathbb {Z}/nmathbb {Z})，给出G≤G表示an (a)的定义。b) (a,b) -纠缠，并给出G G表示已解释或未解释(a,b) (a,b) -纠缠的附加标准。利用这些新定义，我们确定了元组((p,q)，T) ((p,q)，T)，其中p>q∈Z p>qin mathbb {Z}是不同素数，且T T是有限群，使得在Q mathbb {Q}上存在无限多条非Q¯overline {mathbb {Q}} -同构椭圆曲线，且具有未解释的(p, Q) (p, Q) -类型为T的纠缠。进一步，对于纠缠能级(p,q) (p,q)和类型T T的每种可能组合，我们通过构造相应的模曲线和j j -映射，对q mathbb {q}上定义的椭圆曲线进行完全分类。

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引用次数: 11

Separable integer partition classes 可分离整数划分类

Transactions of the American Mathematical Society, Series B

Pub Date : 2020-08-14 DOI: 10.1090/btran/87

G. Andrews

A classical method for partition generating function is developed into a tool with wide applications. New expansions of well-known theorems are derived, and new results for partitions with n n copies of n n are presented.

将一种经典的分区生成函数方法发展成为一种具有广泛应用价值的工具。得到了一些已知定理的新展开式，并给出了n个n个副本的分区的新结果。

引用次数: 4

Rank varieties and 𝜋-points for elementary supergroup schemes 初等超群方案的秩变异和𝜋-points

Transactions of the American Mathematical Society, Series B

Pub Date : 2020-08-06 DOI: 10.1090/btran/74

D. Benson, S. Iyengar, H. Krause, J. Pevtsova

We develop a support theory for elementary supergroup schemes, over a field of positive characteristic p ⩾ 3 pgeqslant 3 , starting with a definition of a π pi -point generalising cyclic shifted subgroups of Carlson for elementary abelian groups and π pi -points of Friedlander and Pevtsova for finite group schemes. These are defined in terms of maps from the graded algebra k [ t , τ ] / ( t p − τ 2 ) k[t,tau ]/(t^p-tau ^2) , where t t has even degree and τ tau has odd degree. The strength of the theory is demonstrated by classifying the pa

我们为初等超群方案开发了一个支持理论，在一个正特征p小于3 p geqslant 3的域上，从Carlson的初等阿贝尔群的π pi点广义循环位移子群和Friedlander和Pevtsova的π pi点的有限群方案的定义开始。这些是根据渐变代数k[t， τ]/(t p−τ 2) k[t, tau]/(t^p- tau ^2)的映射定义的，其中t t具有偶数次，τ tau具有奇数次。通过对一类初等超群格式的稳定模范畴的奇偶变不变定域子范畴进行分类，证明了该理论的强度。

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引用次数: 4

Uniqueness in Cauchy problems for diffusive real-valued strict local martingales 扩散实值严格局部鞅Cauchy问题的唯一性

Transactions of the American Mathematical Society, Series B

Pub Date : 2020-07-29 DOI: 10.1090/btran/141

U. Çetin, Kasper Larsen

For a real-valued one dimensional diffusive strict local martingale, we provide a set of smooth functions in which the Cauchy problem has a unique classical solution under a local 1 2 frac 12 -Hölder condition. Under the weaker Engelbert-Schmidt conditions, we provide a set in which the Cauchy problem has a unique weak solution. We exemplify our results using quadratic normal volatility models and the two dimensional Bessel process.

对于一个实值一维扩散严格局部鞅，我们给出了柯西问题在局部12 frac 12 -Hölder条件下具有唯一经典解的光滑函数集。在较弱的Engelbert-Schmidt条件下，我们给出了柯西问题有唯一弱解的集合。我们使用二次正态波动模型和二维贝塞尔过程来举例说明我们的结果。

引用次数: 1

Dini derivatives and regularity for exchangeable increment processes 可交换增量过程的Dini导数和正则性

Transactions of the American Mathematical Society, Series B

Pub Date : 2020-06-25 DOI: 10.1090/btran/44

O. A. Hernández, Gerónimo Uribe Bravo

. Let X be an exchangeable increment (EI) process whose sample paths are of inﬁnite variation. We prove that for any ﬁxed t almost surely, limsup h Ñ 0 ˘ p X t ` h ´ X t q{ h “ 8 and limsup h Ñ 0 ˘ p X t ` h ´ X t q{ h “ ´8 . This extends a celebrated result of Rogozin for L´evy processes obtained in 1968 and completes the known picture for ﬁnite-variation EI processes. Applications are numerous. For example, we deduce that both half-lines p´8 , 0 q and p 0 , 8q are visited immediately for inﬁnite variation EI processes (called upward and downward regularity). We also generalize the zero-one law of Mil- lar for L´evy processes by showing continuity of X when it reaches its minimum in the inﬁnite variation EI case; an analogous result for all EI processes links right and left continuity at the minimum with upward and downward regularity. We also consider results of Durrett, Iglehart, and Miller on the weak convergence of conditioned Brownian bridges to the normalized Brownian excursion considered in [DIM77] and broadened to a subclass of L´evy processes and EI processes by Chaumont and the second author. We prove it here for all inﬁnite variation EI processes. We furthermore obtain a description of the convex minorant known for L´evy processes found in [Ann. Prob. 40 (2012), pp. 1636–1674] and extend it to non-piecewise linear EI processes. Our main tool to study the Dini derivatives is a change of measure for EI processes which extends the Esscher transform for L´evy processes.

．设X是一个可交换增量(EI)过程，其样本路径是无限变化的。我们证明，对于几乎可以肯定的任何固定t, limsup Ñ 0 × p X t ' h ' X t q{h " 8和limsup Ñ 0 × p X t ' h ' X t q{h " 8。这扩展了Rogozin在1968年获得的关于L ' evy过程的著名结果，并完成了有限变化EI过程的已知图像。应用程序很多。例如，我们推断，对于无限变化EI过程(称为向上和向下规律性)，可以立即访问半线p´8,0q和p 0,8q。通过证明X在无穷变EI情况下达到最小值时的连续性，我们还推广了L′evy过程的Mil- lar的0 - 1定律;对所有EI过程都有类似的结果，至少具有上下规律性的左右连续性。我们还考虑了Durrett, Iglehart和Miller关于条件布朗桥对[DIM77]中考虑的标准化布朗漂移的弱收敛的结果，并由Chaumont和第二作者扩展到L ' evy过程和EI过程的子类。我们在这里证明了它适用于所有无穷变EI过程。我们进一步得到了在[Ann]中发现的L ' evy过程已知的凸小量的描述。并将其推广到非分段线性EI过程中。我们研究Dini导数的主要工具是EI过程的测度变化，它扩展了L ' evy过程的Esscher变换。

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引用次数: 5

Overgroups of regular unipotent elements in simple algebraic groups 简单代数群中正则单幂元的过群

Transactions of the American Mathematical Society, Series B

Pub Date : 2020-06-18 DOI: 10.1090/btran/72

G. Malle, D. Testerman

We investigate positive-dimensional closed reductive subgroups of almost simple algebraic groups containing a regular unipotent element. Our main result states that such subgroups do not lie inside proper parabolic subgroups unless possibly when their connected component is a torus. This extends the earlier result of Testerman and Zalesski treating connected reductive subgroups.

研究了包含正则单幂元的几乎简单代数群的正维闭约子群。我们的主要结果表明，这些子群不位于固有抛物子群内，除非它们的连通分量是环面。这扩展了Testerman和Zalesski先前处理连接约子群的结果。

引用次数: 2

Distribution of Kloosterman paths to high prime power moduli 高素数功率模的Kloosterman路径分布

Transactions of the American Mathematical Society, Series B

Pub Date : 2020-05-18 DOI: 10.1090/btran/98

Djordje Mili'cevi'c, Sichen Zhang

We consider the distribution of polygonal paths joining the partial sums of normalized Kloosterman sums modulo an increasingly high power p n p^n of a fixed odd prime p p , a pure depth-aspect analogue of theorems of Kowalski–Sawin and Ricotta–Royer–Shparlinski. We find that this collection of Kloosterman paths naturally splits into finitely many disjoint ensembles, each of which converges in law as n → ∞ nto infty to a distinct complex valued random continuous function. We further find that the random series resulting from gluing together these limits for every p p converges in law as p → ∞ pto infty , and that paths joining partial Kloosterman sums acquire a different and universal limiting shape after a modest rearrangement of terms. As the key arithmetic input we prove, using the p p -adic method of stationary phase including highly singular cases, that complete sums of products of arbitrarily many Kloosterman sums to high prime power moduli exhibit either power savings or power alignment in shifts of arguments.

我们考虑了归一化Kloosterman和的部分和以一个越来越高的幂p n p^n模固定奇素数p p的多边形路径的分布，这是Kowalski-Sawin定理和Ricotta-Royer-Shparlinski定理的一个纯深度方面的类比。我们发现这个Kloosterman路径的集合自然地分裂成有限多个不相交的集合，每个集合在n→∞n toinfty上收敛到一个不同的复值随机连续函数。我们进一步发现，将每个p p的这些极限粘合在一起所得到的随机级数规律地收敛为p→∞p toinfty，并且加入部分Kloosterman和的路径在适度重排项后获得了不同的通用极限形状。作为关键的算法输入，我们使用包含高度奇异情况的p - p -进阶平稳相位方法证明了任意多个高素数功率模的Kloosterman和积的完全和在参数的移位中表现出功率节省或功率对齐。

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引用次数: 1

Tilting modules, dominant dimensions and Brauer-Schur-Weyl duality 倾斜模，主导维数和Brauer-Schur-Weyl对偶

Transactions of the American Mathematical Society, Series B

Pub Date : 2020-05-05 DOI: 10.1090/btran/84

Jun Hu, Zhankui Xiao

In this paper we use the dominant dimension with respect to a tilting module to study the double centraliser property. We prove that if A A is a quasi-hereditary algebra with a simple preserving duality and T T is a faithful tilting A A -module, then A A has the double centralizer property with respect to T T . This provides a simple and useful criterion which can be applied in many situations in algebraic Lie theory. We affirmatively answer a question of Mazorchuk and Stroppel by proving the existence of a unique minimal basic tilting module T T over A A for which A = E n d

本文利用倾斜模的优势维数研究了双扶正器的性质。证明了如果A A是一个具有简单保持对偶性的拟遗传代数，T T是一个忠实的倾斜A -模，则A A对T T具有双中心化性质。这提供了一个简单而有用的判据，可应用于代数李理论的许多情况。我们肯定地回答了Mazorchuk和Stroppel的一个问题，证明了在a a上存在一个唯一的最小基本倾斜模T T，其中a = en和en并且a (T) (T) a =End_{End_A(T)}(T)。作为应用，在一定条件下，我们在对偶部分调和张量空间上建立了辛舒尔代数S K S y (m,n) S_K^{sy}(m,n)与Brauer代数B n(-2m)之间的Schur- weyl对偶性。

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引用次数: 1

New bounds for Ryser’s conjecture and related problems Ryser猜想的新边界及相关问题

Transactions of the American Mathematical Society, Series B

Pub Date : 2020-05-01 DOI: 10.1090/btran/92

Peter Keevash, A. Pokrovskiy, B. Sudakov, Liana Yepremyan

A Latin square of order n n is an n × n n times n array filled with n n symbols such that each symbol appears only once in every row or column and a transversal is a collection of cells which do not share the same row, column or symbol. The study of Latin squares goes back more than 200 years to the work of Euler. One of the most famous open problems in this area is a conjecture of Ryser-Brualdi-Stein from 60s which says that every Latin square of order n × n ntimes n contains a transversal of order n − 1 n-1 . In this paper we prove the existence of a transversal of order n − O ( log ⁡ n / log ⁡ log ⁡

A拉丁广场秩序的n n是一个 n × n n 时报阵列充满每n”这样的符号或曾经只出现在每排纵队》和细胞a跨经是收藏哪种不要分享不变row,纵队或象征。对欧拉的研究可以追溯到200多年前。一号》最著名的开放区域problems in this is a conjecture Ryser-Brualdi-Stein从60的哪种拉丁说那每广场的秩序 n × n n 时报跨经contains a的秩序 n−1 n-1。在这篇文章我们证明跨经甲之存在的秩序 n−O ( 日志 ⁡ n / 日志 ⁡ 日志 ⁡ n ) n-O对数(log - {n} - {日志{n}}), improving the celebrated束缚of n−O ( 日志2 ⁡ n ) n-O( ^日志肖尔哈塔米(leila Hatami)和偏2n)。我们的相似之处(与报喜不同)很常见，其他的应用也很好。我们得到a new束缚下城on a 40岁的conjecture Brouwer斯坦在三重系统配套的《maximum,露出那每一个这样的系统配套的订单n n是肯定有百万之大小的 n / 3−O ( 日志 ⁡ n / 日志 ⁡ 日志 ⁡ n ) n / 3-O对数(log - {n} - {日志{n}})。这证实了孤独、金和斯宾塞的说法终于,我们也都显示 O ( log n ⁡ n / 日志 ⁡ 日志 ⁡ n ) O (n 日志{n} - { {n}})许多日志日志”在拉丁语arrays suffice保证跨经a full, improving on百万previously知道束缚的 n 2−ε n ^ {2 - varepsilon}。《小说proofs联合in a way semi-random方法和《edge-coloured robust财产哦稍等在一起pseudorandom graphs展示covering所有,但配套的彩虹之存在 O ( 日志 ⁡ n / 日志 ⁡ 日志 ⁡ n ) O (log log n / { {n}}) vertices日志。所有previous results,改编自《semi-random方法,左边一个保姆至少 Ω ( n α

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引用次数: 24

Chudnovsky’s conjecture and the stable Harbourne–Huneke containment Chudnovsky猜想与稳定的Harbourne-Huneke容器

Transactions of the American Mathematical Society, Series B

Pub Date : 2020-04-23 DOI: 10.1090/btran/103

Sankhaneel Bisui, Eloísa Grifo, Huy Tài Hà, Thai Thanh Nguyen

We investigate containment statements between symbolic and ordinary powers and bounds on the Waldschmidt constant of defining ideals of points in projective spaces. We establish the stable Harbourne conjecture for the defining ideal of a general set of points. We also prove Chudnovsky’s Conjecture and the stable version of the Harbourne–Huneke containment conjectures for a general set of sufficiently many points.

研究了定义射影空间中点的理想的Waldschmidt常数的符号幂与普通幂之间的包含命题和界。对于一般点集的定义理想，我们建立了稳定的Harbourne猜想。对于一个足够多的点的一般集合，我们也证明了Chudnovsky猜想和Harbourne-Huneke包容猜想的稳定版本。

引用次数: 14

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