Bulletin of the London Mathematical Society最新文献

{"title":"Asymptotic Behavior of the Bergman Metric at Infinite Type Points","authors":"Ravi Shankar Jaiswal","doi":"10.1112/blms.70100","DOIUrl":"10.1112/blms.70100","url":null,"abstract":"<p>We investigate nontangential asymptotic limits of the Bergman kernel on the diagonal, and the Bergman metric and its holomorphic sectional curvature at exponentially flat infinite-type boundary points of smooth bounded pseudoconvex domains in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$mathbb {C}^{n + 1}$</annotation>\u0000 </semantics></math>, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>∈</mo>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 <annotation>$n in mathbb {N}$</annotation>\u0000 </semantics></math>. After showing that these objects satisfy the appropriate localizations, we apply the method of scaling to prove our results.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 8","pages":"2372-2394"},"PeriodicalIF":0.9,"publicationDate":"2025-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144815214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Eigenvalue estimate for the \u0000 \u0000 p\u0000 $p$\u0000 -Laplace operator on a connected finite graph","authors":"Lin Feng Wang","doi":"10.1112/blms.70104","DOIUrl":"10.1112/blms.70104","url":null,"abstract":"<p>In this paper, we consider eigenvalue estimate for the <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-Laplace operator <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>▵</mi>\u0000 <mi>p</mi>\u0000 </msub>\u0000 <annotation>$triangle _p$</annotation>\u0000 </semantics></math> on a connected finite graph with the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>CD</mi>\u0000 <mi>p</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>m</mi>\u0000 <mo>,</mo>\u0000 <mn>0</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathrm{CD}_p(m,0)$</annotation>\u0000 </semantics></math> condition for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$p&gt;1$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$m&gt;0$</annotation>\u0000 </semantics></math>. We first establish elliptic gradient estimates for solutions to the eigenvalue equation. Then we establish a lower bound estimate for the first nonzero eigenvalue of <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>▵</mi>\u0000 <mi>p</mi>\u0000 </msub>\u0000 <annotation>$triangle _p$</annotation>\u0000 </semantics></math>, which is a generalization not only of the eigenvalue estimate for the manifold setting, but also of the eigenvalue estimate for the <span></span><math>\u0000 <semantics>\u0000 <mi>μ</mi>\u0000 <annotation>$mu$</annotation>\u0000 </semantics></math>-Laplace operator <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>▵</mi>\u0000 <mi>μ</mi>\u0000 </msub>\u0000 <annotation>$triangle _{mu }$</annotation>\u0000 </semantics></math> on the graph with the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>CD</mi>\u0000 <mo>(</mo>\u0000 <mi>m</mi>\u0000 <mo>,</mo>\u0000 <mn>0</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathrm{CD}(m,0)$</annotation>\u0000 </semantics></math> condition.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 8","pages":"2444-2461"},"PeriodicalIF":0.9,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144815241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dual matroids of 2-complexes — Revisited","authors":"Johannes Carmesin","doi":"10.1112/blms.70077","DOIUrl":"10.1112/blms.70077","url":null,"abstract":"<p>We prove that simply connected local two-dimensional simplicial complexes embed in 3-space if and only if their dual matroids are graphic. Examples are provided that the assumptions of simply connectedness and locality are necessary. This may be regarded as a three-dimensional analogue of Whitney's planarity criterion from 1932.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 7","pages":"2033-2044"},"PeriodicalIF":0.9,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144681336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Natário's Minkowski-type inequality in the hyperbolic space","authors":"Yong Wei","doi":"10.1112/blms.70106","DOIUrl":"10.1112/blms.70106","url":null,"abstract":"<p>We apply Brendle–Guan–Li's inverse curvature–type flow to prove a family of sharp inequalities for curvature integrals and their rigidity results for hypersurfaces in the hyperbolic space. In particular, we provide a new short proof of Natário's Minkowski-type inequality and its rigidity for convex surfaces in the hyperbolic 3-space.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 8","pages":"2477-2488"},"PeriodicalIF":0.9,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144815240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Artin's conjecture on average and short character sums","authors":"Oleksiy Klurman,&nbsp;Igor E. Shparlinski,&nbsp;Joni Teräväinen","doi":"10.1112/blms.70103","DOIUrl":"10.1112/blms.70103","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>N</mi>\u0000 <mi>a</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$N_a(x)$</annotation>\u0000 </semantics></math> denote the number of primes up to <span></span><math>\u0000 <semantics>\u0000 <mi>x</mi>\u0000 <annotation>$x$</annotation>\u0000 </semantics></math> for which the integer <span></span><math>\u0000 <semantics>\u0000 <mi>a</mi>\u0000 <annotation>$a$</annotation>\u0000 </semantics></math> is a primitive root. We show that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>N</mi>\u0000 <mi>a</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$N_a(x)$</annotation>\u0000 </semantics></math> satisfies the asymptotic predicted by Artin's conjecture for almost all <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>⩽</mo>\u0000 <mi>a</mi>\u0000 <mo>⩽</mo>\u0000 <mi>exp</mi>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>log</mi>\u0000 <mi>log</mi>\u0000 <mi>x</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$1leqslant aleqslant exp ((log log x)^2)$</annotation>\u0000 </semantics></math>. This improves on a result of Stephens (1969). A key ingredient in the proof is a new short character sum estimate over the integers, improving on the range of a result of Garaev (2006).</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 8","pages":"2429-2443"},"PeriodicalIF":0.9,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70103","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144815242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A note on combinatorial invariance of Kazhdan–Lusztig polynomials","authors":"Francesco Esposito,&nbsp;Mario Marietti","doi":"10.1112/blms.70101","DOIUrl":"10.1112/blms.70101","url":null,"abstract":"<p>We introduce the concepts of an amazing hypercube decomposition and a double shortcut for it, and use these new ideas to formulate a conjecture implying the combinatorial invariance conjecture for the Kazhdan–Lusztig polynomials of the symmetric group. This conjecture has the advantage of being combinatorial in nature. The appendix by Barkley and Gaetz discusses the related notion of double hypercubes and proves an analogous conjecture for these in the case of co-elementary intervals.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 8","pages":"2395-2403"},"PeriodicalIF":0.9,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144815137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dimension-free Fourier restriction inequalities","authors":"Diogo Oliveira e Silva,&nbsp;Błażej Wróbel","doi":"10.1112/blms.70098","DOIUrl":"10.1112/blms.70098","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${{bf R}_{mathbb {S}^{d-1}}}(prightarrow q)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; denote the best constant for the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$L^p(mathbb {R}^d)rightarrow L^q(mathbb {S}^{d-1})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; Fourier restriction inequality to the unit sphere &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$mathbb {S}^{d-1}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, and let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;mo&gt;;&lt;/mo&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 ","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 8","pages":"2336-2353"},"PeriodicalIF":0.9,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144815151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Heisenberg uniqueness pairs and the wave equation","authors":"Shanlin Huang,&nbsp;Jiaqi Yu","doi":"10.1112/blms.70095","DOIUrl":"10.1112/blms.70095","url":null,"abstract":"&lt;p&gt;The concept of the Heisenberg uniqueness pair &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;Γ&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;Λ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(Gamma, Lambda)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; was introduced by Hedenmalm and Montes-Rodríguez as a variant of the uncertainty principle for the Fourier transform. The main results in Hedenmalm and Montes-Rodríguez (Ann. of Math. (2) &lt;b&gt;173&lt;/b&gt; (2011), 1507–1527) concern the hyperbola &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Γ&lt;/mi&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;mo&gt;}&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Gamma _{epsilon }=lbrace (x_1, x_2)in mathbb {R}^2,, x_1x_2=epsilon rbrace$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; (&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;≠&lt;/mo&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$0ne epsilon in mathbb {R}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;) and lattice-crosses &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Λ&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;mi&gt;β&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 &lt;mo&gt;×&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 8","pages":"2286-2310"},"PeriodicalIF":0.9,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144814589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the stack of 0-dimensional coherent sheaves: Motivic aspects","authors":"Barbara Fantechi,&nbsp;Andrea T. Ricolfi","doi":"10.1112/blms.70096","DOIUrl":"10.1112/blms.70096","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;annotation&gt;$X$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a variety. In this survey, we study (decompositions of) the motivic class, in the Grothendieck ring of stacks, of the stack &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;mi&gt;o&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;h&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathcal {C}hspace{-2.5pt}{o}hspace{-1.99997pt}{h}^n(X)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of 0-dimensional coherent sheaves of length &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;annotation&gt;$n$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; on &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;annotation&gt;$X$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. To do so, we review the construction of the support map &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;mi&gt;o&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;h&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mo&gt;Sym&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathcal {C}hspace{-2.5pt}{o}hspace{-1.99997pt}{h}^n(X) rightarrow operatorname{Sym}^n(X)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; to the symmetric product and we prove that, for any closed point &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$p in X$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, the motive of the punctual stack &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;mi&gt;o&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;h&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 ","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 6","pages":"1607-1649"},"PeriodicalIF":0.9,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70096","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144245008","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Graphical models for topological groups: A case study on countable Stone spaces","authors":"Beth Branman,&nbsp;George Domat,&nbsp;Hannah Hoganson,&nbsp;Robert Alonzo Lyman","doi":"10.1112/blms.70097","DOIUrl":"10.1112/blms.70097","url":null,"abstract":"<p>By analogy with the Cayley graph of a group with respect to a finite generating set or the Cayley–Abels graph of a totally disconnected, locally compact group, we detail countable connected graphs associated to Polish groups that we term Cayley–Abels–Rosendal graphs. A group admitting a Cayley–Abels–Rosendal graph acts on it continuously, coarsely metrically properly and cocompactly by isometries of the path metric. By an expansion of the Milnor–Schwarz lemma, it follows that the group is generated by a coarsely bounded set and the group equipped with a word metric with respect to a coarsely bounded generating set and the graph are quasi-isometric. In other words, groups admitting Cayley–Abels–Rosendal graphs are topological analogues of finitely generated groups. Our goal is to introduce this topological perspective on the work of Rosendal to a geometric group theorist. We apply these concepts to homeomorphism groups of countable Stone spaces. We completely characterize when these homeomorphism groups are coarsely bounded, when they are locally bounded (all of them are), and when they admit a Cayley–Abels–Rosendal graph, and if so produce a coarsely bounded generating set.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 8","pages":"2311-2335"},"PeriodicalIF":0.9,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70097","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144814616","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}