Journal of the London Mathematical Society-Second Series最新文献

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The m $m$ -step solvable anabelian geometry of mixed-characteristic local fields 混合特征局部场的m$ m$ -步可解的阿贝尔几何

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series

Pub Date : 2025-12-22 DOI: 10.1112/jlms.70402

Seung-Hyeon Hyeon

Let <math> <semantics> <mi>K</mi> <annotation>$K$</annotation> </semantics></math> be a mixed-characteristic local field. For an integer <math> <semantics> <mrow> <mi>m</mi> <mo>⩾</mo> <mn>0</mn> </mrow> <annotation>$m geqslant 0$</annotation> </semantics></math>, we denote by <math> <semantics> <mrow> <msup> <mi>K</mi> <mi>m</mi> </msup> <mo>/</mo> <mi>K</mi> </mrow> <annotation>$K^m / K$</annotation> </semantics></math> the maximal <math> <semantics> <mi>m</mi> <annotation>$m$</annotation> </semantics></math>-step solvable extension of <math> <semantics> <mi>K</mi> <annotation>$K$</annotation> </semantics></math>, and by <math> <semantics> <msubsup> <mi>G</mi> <mi>K</mi> <mi>m</mi> </msubsup> <annotation>$G_K^m$</annotation> </semantics></math> the maximal <math> <semantics> <mi>m</mi> <annotation>$m$</annotation> </semantics></math>-step solvable quotient of the absolute Galois group <math> <semantics> <msub> <mi>G</mi> <mi>K</mi> </msub> <annotation>$G_K$</annotation> </semantics></math> of <math> <semantics> <mi>K</mi> <annotation>$K$</annotation> </semantics></math>. We regard <math> <semantics> <msub> <mi>G</mi> <mi>K</mi> </msub> <annotation>$G_K$</annotation> </semantics></math> and its quotients as filtered profinite groups via the respective upper-numbering ramification filtrations. It is known from the previous result due to Mochizuki that the isomorphism class of <math> <semantics> <mi>K</mi> <annotation>$K$</annotation> </semantics></math> is determined by the isomorphism class of the filtered profinite group <math> <semantics> <msub> <mi>G</mi> <mi>K</mi>

设K $K$为混合特征局部域。对于整数m或0 $m geqslant 0$，我们用K m / K $K^m / K$表示K $K$的最大m $m$阶跃可解扩展，并由gkm $G_K^m$求绝对伽罗瓦群gk$G_K$的最大m $m$步可解商K $K$。我们把gk $G_K$和它的商看作是通过各自的上数分支过滤的无限群。由先前Mochizuki的结果可知，K $K$的同构类是由滤过的无限群G K $G_K$的同构类决定的。证明了K $K$的同构类是由最大2步可解商gk2 $G_K^2$的同构类作为一个过滤的无限群决定的，进而证明了K 的同构类是由最大2步可解商gk2 的同构类决定的。K m / K $K^m / K$由滤过的无限群G K m + 2函数决定$G_K^{m + 2}$(分别；G K m + 3 $G_K^{m + 3}$)对于m小于2 $m geqslant 2$(分别，M = 0,1 $m = 0, 1$)。

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引用次数: 0

Euclidean algorithms are Gaussian over imaginary quadratic fields 欧几里得算法是虚二次域上的高斯算法

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series

Pub Date : 2025-12-20 DOI: 10.1112/jlms.70333

Dohyeong Kim, Jungwon Lee, Seonhee Lim

We prove that the distribution of the number of steps of the Euclidean algorithm of rationals in imaginary quadratic fields with denominators bounded by $� � N � �$ is asymptotically Gaussian as $� � N � �$ goes to infinity, extending a result by Baladi and Vallée for the real case. The proof is based on the spectral analysis of the transfer operator associated to the nearest integer complex continued fraction map, which is piecewise analytic and expanding but not a full branch map. By observing a finite Markov partition with a regular CW-structure, which enables us to associate the transfer operator acting on a direct sum of spaces of $� � �^{C � 1 �} � �$ -functions, we obtain the limit Gaussian distribution as well as residual equidistribution.

证明了在以N$ N$为界的虚二次域上，当N$ N$趋于无穷时，欧几里得有序数算法的步数分布渐近高斯分布，推广了Baladi和vallsamei的结果。该证明基于最近整数复连分数映射的传递算子谱分析，该映射是分段解析和展开的，但不是全分支映射。通过观察具有正则cw结构的有限马尔可夫配分，使我们能够将作用于c1 $C^1$ -函数空间的直接和的传递算子联系起来，我们得到了极限高斯分布和残差等分布。

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引用次数: 0

Extremal number of cliques of given orders in graphs with a forbidden clique minor 具有禁止小团的图中给定阶的小团的极值数目

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series

Pub Date : 2025-12-19 DOI: 10.1112/jlms.70399

Ruilin Shi, Fan Wei

Alon and Shikhelman initiated the systematic study of a generalization of the extremal function. Motivated by algorithmic applications, the study of the extremal function <math> <semantics> <mrow> <mtext>ex</mtext> <mo>(</mo> <mi>n</mi> <mo>,</mo> <msub> <mi>K</mi> <mi>k</mi> </msub> <mo>,</mo> <msub> <mi>K</mi> <mi>t</mi> </msub> <mtext>-minor</mtext> <mo>)</mo> </mrow> <annotation>$text{ex}(n, K_k, K_ttext{-minor})$</annotation> </semantics></math>, that is, the number of cliques of order <math> <semantics> <mi>k</mi> <annotation>$k$</annotation> </semantics></math> in <math> <semantics> <msub> <mi>K</mi> <mi>t</mi> </msub> <annotation>$K_t$</annotation> </semantics></math>-minor free graphs on <math> <semantics> <mi>n</mi> <annotation>$n$</annotation> </semantics></math> vertices, has received much attention. In this paper, we determine essentially sharp bounds on the maximum possible number of cliques of order <math> <semantics> <mi>k</mi> <annotation>$k$</annotation> </semantics></math> in a <math> <semantics> <msub> <mi>K</mi> <mi>t</mi> </msub> <annotation>$K_t$</annotation> </semantics></math>-minor free graph on <math> <semantics> <mi>n</mi> <annotation>$n$</annotation> </semantics></math> vertices. More precisely, we determine a function <math> <semantics> <mrow> <mi>C</mi> <mo>(</mo> <mi>k</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <annotation>$C(k,t)$</annotation> </semantics></math> such that for each <math> <semantics> <mrow> <mi>k</mi> <mo><</mo> <mi>t</mi> </mrow> <annotation>$k < t$</annotation> </semantics></math> with <math> <semantics> <mrow> <mi>t</mi> <mo>−</mo> <mi>k</mi> <mo>≫</mo> <msub> <mi

Alon和Shikhelman开创了对极值函数推广的系统研究。受算法应用的启发，研究极值函数ex (n, K K, K t -minor)$ text{ex}(n, K_k, K_ttext{-minor})$，即在k$ t$ K_t$ -次自由图中n$ n$个顶点上k$ k$阶团的数目受到了广泛的关注。在本文中，我们确定了在n$ n$顶点上的k$ t$ K_t$ -次自由图中k$ k$阶团的最大可能数目的本质上的尖锐界限。更准确地说，我们确定一个函数C (k)t)$ C(k,t)$使得对于每一个k <； t$ k < t$与t−k ^ log 2 t$ t-kgg log2 t$，每个K t$ K_t$ -次自由图在n$ n$顶点上最多有n个C (K)t) 1 + 0 t (1) $ n C(k，T)^{1+o_t(1)}$ k阶的团$k$。我们也证明了这个界限是清晰的通过在n n个顶点上构造一个kt_k_t无次元图C(K, t) n$ C(K)T) n个k阶的团。这个界限回答了Wood和Fox-Wei在指数中渐近到0 t(1)$ o_t(1)$的问题，除了k$ k$非常接近t$ t$时的极值。

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引用次数: 0

Jet schemes of local complete intersection morphisms 局部完全交态射的射流格式

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series

Pub Date : 2025-12-19 DOI: 10.1112/jlms.70393

Andrew R. Stout

The focus of this paper is to describe the conditions for which the generalized jet operator <math> <semantics> <mrow> <msub> <munder> <mrow> <mi>H</mi> <mi>o</mi> <mi>m</mi> </mrow> <mo>̲</mo> </munder> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>Z</mi> <mo>,</mo> <mo>−</mo> <mo>)</mo> </mrow> </mrow> <annotation>$underline{Hom}_k(Z, -)$</annotation> </semantics></math> induces a local complete intersection morphism <math> <semantics> <mrow> <mover> <mi>f</mi> <mo>̂</mo> </mover> <mo>:</mo> <msub> <munder> <mrow> <mi>H</mi> <mi>o</mi> <mi>m</mi> </mrow> <mo>̲</mo> </munder> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>Z</mi> <mo>,</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>→</mo> <msub> <munder> <mrow> <mi>H</mi> <mi>o</mi> <mi>m</mi> </mrow> <mo>̲</mo> </munder> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>Z</mi> <mo>,</mo> <mi>S</mi> <mo>)</mo> </mrow> </mrow> <annotation>$hat{f}: underline{Hom}_k(Z, X) rightarrow underline{Hom}_k(Z, S)$</annotation> </semantics></math> given a local complete intersection morphism <math> <semantics> <mrow> <mi>f</mi> <mo>:</mo> <mi>X</mi> <mo>→</mo> <mi>S</mi> </mrow> <annotation>$f: Xrightarrow S$</annotation> </semantics></math> of separated locally finite type schemes over a field <math> <semantics> <mi>k</mi> <annotation>$k$</annotation> </semantics></mat

本文的重点是描述广义射流算子H o m ＿ k (Z，−)$underline{Hom}_k(Z, -)$导出一个局部完全交态f ？我是谁？X)→H ＿ m ＿ k (Z，S) $hat{f}: underline{Hom}_k(Z, X) rightarrow underline{Hom}_k(Z, S)$给定一个局部完全交态f：域k $k$上分离的局部有限型格式的X→S $f: Xrightarrow S$，其中S $S$可能是一个非约简格式。我们还考虑了诱导态射f¯的更一般的条件：L Z (X)→L Z (S) $bar{f}: mathcal {L}_Z(X) rightarrow mathcal {L}_Z(S)$之间对应的化简诱导闭合子方案结构是一个局部完全交态射。

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引用次数: 0

Nonexistence of solutions to classes of parabolic inequalities in the Riemannian setting 黎曼环境下抛物型不等式类解的不存在性

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series

Pub Date : 2025-12-19 DOI: 10.1112/jlms.70394

Dorothea-Enrica von Criegern, Gabriele Grillo, Dario D. Monticelli

We establish conditions for nonexistence of global solutions for a class of quasilinear parabolic problems with a potential on complete, non-compact Riemannian manifolds, including the Porous Medium Equation and the p-Laplacian with a potential term. Our results reveal the interplay between the manifold's geometry, the power nonlinearity, and the potential's behavior at infinity. Using a test function argument, we identify explicit parameter ranges where nonexistence holds.

本文建立了一类在完全非紧黎曼流形上具有势的拟线性抛物型问题整体解不存在的条件，包括多孔介质方程和带势项的p-拉普拉斯方程。我们的结果揭示了流形几何、幂非线性和无穷远处势的行为之间的相互作用。使用测试函数实参，我们明确地标识不存在的形参范围。

引用次数: 0

On the solvability of the Lie algebra HH 1 ( B ) $mathrm{HH}^1(B)$ for blocks of finite groups 李代数HH 1(B)$ mathm {HH}^1(B)$对有限群块的可解性

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series

Pub Date : 2025-12-19 DOI: 10.1112/jlms.70407

Markus Linckelmann, Jialin Wang

We give some criteria for the Lie algebra $� � � �^{HH � 1 �} � � (� B �) � � � �$ to be solvable, where $� � B � �$ is a $� � p � �$ -block of a finite group algebra, in terms of the action of an inertial quotient of $� � B � �$ on a defect group of $� � B � �$ .

给出了李代数HH 1(B)$ mathm {HH}^1(B)$的可解准则。其中B$ B$是有限群代数中的p$ p$ -块，表示B$ B$的惯性商作用于B$ B$的缺陷群。

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引用次数: 0

Averages of determinants of Laplacians over moduli spaces for large genus 大属模空间上拉普拉斯算子行列式的平均

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series

Pub Date : 2025-12-18 DOI: 10.1112/jlms.70395

Yuxin He, Yunhui Wu

Let $� � �_{M � g �} � �$ be the moduli space of hyperbolic surfaces of genus $� � g � �$ endowed with the Weil–Petersson metric. We view the regularized determinant $� � � \log � det � (� �_{Δ � X �} �) � � �$ of Laplacian as a function on $� � �_{M � g �} � �$ and show that there exists a universal constant $� � � E � > � 0 � � �$ such that as $� � � g � \to � \infty � � �$ ,

设M g $mathcal {M}_g$为具有Weil-Petersson度规的g $g$属双曲曲面的模空间。我们把拉普拉斯算子的正则化行列式log det （Δ X） $log det (Delta _{X})$看作是M g $mathcal {M}_g$上的一个函数，并证明存在一个普适常数E ＆gt; 0 $E>0$令g→∞$grightarrow infty$，

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引用次数: 0

Local–global principles for semi-integral points on Markoff orbifold pairs Markoff轨道对上半积分点的局部-全局原理

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series

Pub Date : 2025-12-18 DOI: 10.1112/jlms.70363

Vladimir Mitankin, Justin Uhlemann

We study local–global principles for semi-integral points on orbifold pairs of Markoff type. In particular, we analyse when these orbifold pairs satisfy weak weak approximation, weak approximation and strong approximation off a finite set of places. We show that Markoff orbifold pairs satisfy the semi-integral Hasse principle and we measure how often such orbifold pairs have strict semi-integral points but the corresponding Markoff surface lacks integral points.

研究了Markoff型轨道对上半积分点的局部-全局原理。特别地，我们分析了这些轨道对在有限位置上满足弱、弱逼近、弱逼近和强逼近的条件。我们证明了Markoff轨道对满足半积分哈塞原理，并测量了这种轨道对具有严格的半积分点而对应的Markoff曲面缺乏积分点的频率。

引用次数: 0

Tambara–Yamagami categories over the reals: The nonsplit case 实数上的Tambara-Yamagami分类：非分裂情况

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series

Pub Date : 2025-12-17 DOI: 10.1112/jlms.70355

Julia Plavnik, Sean Sanford, Dalton Sconce

Tambara and Yamagami investigated a simple set of fusion rules with only one noninvertible object, and proved under which circumstances those rules could be given a coherent associator. They also classified all of the resulting fusion categories up to monoidal equivalence. We consider a generalization of such fusion rules to the setting where simple objects are no longer required to be split simple. Over the real numbers, this means that simple objects are either real, complex, or quaternionic. In this context, we prove a similar categorification result to the one of Tambara and Yamagami.

Tambara和Yamagami研究了一组只有一个不可逆对象的简单融合规则，并证明了在什么情况下这些规则可以被给定一个相干的结合子。他们还将所有产生的融合类别分类到单轴等效。我们考虑将这种融合规则推广到不再需要拆分简单对象的情况。对于实数，这意味着简单对象要么是实数，要么是复数，要么是四元数。在此背景下，我们证明了一个与Tambara和Yamagami相似的分类结果。

引用次数: 0

Torsion in Kauffman bracket skein module of a 4-strand Montesinos knot exterior 四股蒙特西诺斯结外部的考夫曼托架绞丝模的扭转

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series

Pub Date : 2025-12-17 DOI: 10.1112/jlms.70398

Haimiao Chen

For an oriented 3-manifold <math> <semantics> <mi>M</mi> <annotation>$M$</annotation> </semantics></math>, let <math> <semantics> <mrow> <mi>S</mi> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> <annotation>$mathcal {S}(M)$</annotation> </semantics></math> denote its Kauffman bracket skein module over <math> <semantics> <mrow> <mi>Z</mi> <mo>[</mo> <msup> <mi>q</mi> <mrow> <mo>±</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mo>]</mo> </mrow> <annotation>$mathbb {Z}[q^{pm frac{1}{2}}]$</annotation> </semantics></math>. We show that <math> <semantics> <mrow> <mi>S</mi> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> <annotation>$mathcal {S}(M)$</annotation> </semantics></math> admits torsion when <math> <semantics> <mi>M</mi> <annotation>$M$</annotation> </semantics></math> is the exterior of the Montesinos knot <math> <semantics> <mrow> <mi>K</mi> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>/</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <mo>/</mo> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>a</mi> <mn>3</mn> </msub> <mo>/</mo> <msub> <mi>b</mi> <mn>4</mn> </msub> <mo>,</mo> <msub> <mi>a</mi> <mn>4</mn> </msub> <mo>/</mo> <msub> <mi>b</mi> <mn>4</mn> </msub> <mo>)</mo> </mrow> <annotation>$K(a_1/b_1,a_2/b_2,a_3/b_4,a_4/b_4)$</annota

对于一个定向3-歧管M $M$，设S (M) $mathcal {S}(M)$表示其在Z [q±12]上的Kauffman托架绞丝模$mathbb {Z}[q^{pm frac{1}{2}}]$。我们证明当M $M$是蒙特西诺斯结K （a 1 /）的外部时S (M) $mathcal {S}(M)$允许扭转b1, a2 / b2, a3 / b2，A 4 / b 4) $K(a_1/b_1,a_2/b_2,a_3/b_4,a_4/b_4)$每个b I大于或等于3 $b_igeqslant 3$。这为Kirby列表中的问题1.92 (G) - (i)提供了一个否定的答案，该问题询问当M $M$不可约且没有不可压缩的无边界平行环面时S (M) $mathcal {S}(M)$是否自由。

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