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

{"title":"Regulator constants and cohomology","authors":"Luca Caputo","doi":"10.1112/jlms.70671","DOIUrl":"https://doi.org/10.1112/jlms.70671","url":null,"abstract":"<p>We show how regulator constants of a finitely generated <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Z</mi>\u0000 <mo>[</mo>\u0000 <mi>G</mi>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <annotation>$mathbb {Z}[G]$</annotation>\u0000 </semantics></math>-module can be related to <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>-cohomology, where <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> is a finite group. We then derive consequences of this relation for modules naturally arising in number theory, such as rings of integers and units of number fields, <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math>-theory groups of rings of integers and Mordell–Weil groups of elliptic curves.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148816669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A generalisation of Cameron's base size conjecture","authors":"Marina Anagnostopoulou-Merkouri","doi":"10.1112/jlms.70651","DOIUrl":"https://doi.org/10.1112/jlms.70651","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;mi&gt;G&lt;/mi&gt;\u0000 &lt;mo&gt;⩽&lt;/mo&gt;\u0000 &lt;mi&gt;Sym&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Gleqslant {rm Sym}(Omega)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a finite transitive permutation group with point stabiliser &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;annotation&gt;$H$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. A base for &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;annotation&gt;$G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a subset of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;annotation&gt;$Omega$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; whose pointwise stabiliser is trivial, and the minimal cardinality of a base is called the base size of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;annotation&gt;$G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, denoted by &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;b&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$b(G, Omega)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Equivalently, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;b&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$b(G, Omega)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is the minimal positive integer &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;annotation&gt;$k$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; such that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;annotation&gt;$G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; has a regular orbit on the Cartesian product &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$Omega ^k$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. A well-known conjecture of Cameron from the 1990s asserts that if &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;annotation&gt;$G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is an almost simple primitive group and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70651","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148848647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Operator symmetric moduli and sharp triangle inequalities","authors":"Teng Zhang","doi":"10.1112/jlms.70672","DOIUrl":"https://doi.org/10.1112/jlms.70672","url":null,"abstract":"&lt;p&gt;For &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Zin mathbb {M}_n$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, we compare the usual operator right modulus with two natural symmetric variants, the arithmetic symmetric modulus &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;sym&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 &lt;mo&gt;∗&lt;/mo&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$|Z|_{mathrm{sym}}:=(|Z|+|Z^*|)/2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and the quadratic symmetric modulus &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;qsym&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 &lt;mo&gt;∗&lt;/mo&gt;\u0000 &lt;/msup&gt;\u0000 &lt;msup&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mfenced&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$|Z|_{mathrm{qsym}}:=left((|Z|^2+|Z^*|^2)/2right)^{frac{1}{2}}$&lt;/annotation&gt;\u0000 &lt;/sema","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148754014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"How to see the forest despite the trees","authors":"Erika Bérczi-Kovács,&nbsp;András Frank","doi":"10.1112/jlms.70668","DOIUrl":"https://doi.org/10.1112/jlms.70668","url":null,"abstract":"<p>One of the major starting points of discrete optimization is the theorem of Nash-Williams and Tutte on the existence of <span></span><math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math> disjoint spanning trees of a graph, along with its counterpart on the existence of <span></span><math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math> forests covering all edges of the graph. These elegant results triggered comprehensive research that gave rise to far-reaching generalizations and found applications in seemingly distant areas. Our first goal is to elucidate some aspects of these developments with the hope that the story finds its way to nonexperts. But we hope that experts will also find some novelty in our exposition.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70668","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"KdV limit for the Vlasov–Poisson–Landau system","authors":"Renjun Duan,&nbsp;Dongcheng Yang,&nbsp;Hongjun Yu","doi":"10.1112/jlms.70667","DOIUrl":"https://doi.org/10.1112/jlms.70667","url":null,"abstract":"<p>We are concerned with the fluid limit to KdV equations for the one-dimensional Vlasov–Poisson–Landau system that describes the dynamics of ions in plasma with the electron density determined by the self-consistent electric potential through the so-called Boltzmann relation. Formally, it is well known that as the Knudsen number <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ε</mi>\u0000 <mo>→</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$varepsilon rightarrow 0$</annotation>\u0000 </semantics></math> the Vlasov–Poisson–Landau system in the compressible scaling converges to the Euler–Poisson equations which further under the Gardner–Morikawa transformation\u0000\u0000 </p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70667","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hilbert schemes of elliptic surfaces: Group actions and derived categories","authors":"David Zhiyuan Bai","doi":"10.1112/jlms.70663","DOIUrl":"https://doi.org/10.1112/jlms.70663","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;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Xrightarrow C$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be an elliptic surface with integral fibers and a section. The Hilbert scheme &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;[&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;]&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$X^{[n]}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; fibers over &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;[&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;]&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$C^{[n]}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. We construct a commutative group scheme over the entire base &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;[&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;]&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$C^{[n]}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; that embeds as an open subscheme of the Hilbert scheme, such that its action on itself extends to the entirety of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;[&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;]&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$X^{[n]}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. We show that the action is &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;δ&lt;/mi&gt;\u0000 &lt;annotation&gt;$delta$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-regular in the sense of Ngô. Using the derived McKay correspondence, we construct an exact autoequivalence of &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;D&lt;/mi&gt;\u0000 &lt;mi&gt;b&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;Coh&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;[&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;]&lt;/mo&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;$D^boperatorname{Coh}(X^{[n]})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, whose kernel is a maximal Cohen–Macaulay sheaf on the fiber pro","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A trace–path integral formula over function fields","authors":"Yan Yau Cheng","doi":"10.1112/jlms.70664","DOIUrl":"https://doi.org/10.1112/jlms.70664","url":null,"abstract":"<p>We show that an arithmetic path integral over the <span></span><math>\u0000 <semantics>\u0000 <mi>ℓ</mi>\u0000 <annotation>$ell$</annotation>\u0000 </semantics></math>-torsion of a Jacobian <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>J</mi>\u0000 <mo>[</mo>\u0000 <mi>ℓ</mi>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <annotation>$J[ell]$</annotation>\u0000 </semantics></math> is equal to the trace of the Frobenius action on a representation of the Heisenberg group <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 <mo>(</mo>\u0000 <mi>J</mi>\u0000 <mo>[</mo>\u0000 <mi>ℓ</mi>\u0000 <mo>]</mo>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$H(J[ell])$</annotation>\u0000 </semantics></math>, up to an explicitly determined sign. This is an arithmetic analogue of trace–path integral formulae which arise in quantum field theory, where path integrals over a space of sections of a fibration over a circle can be expressed as the trace of the monodromy action on a Hilbert space.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70664","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the deterministic interior body of random polytopes","authors":"Minas Pafis,&nbsp;Natalia Tziotziou","doi":"10.1112/jlms.70665","DOIUrl":"https://doi.org/10.1112/jlms.70665","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msubsup&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;mi&gt;i&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;}&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;annotation&gt;$lbrace X_irbrace _{i=1}^{infty }$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a sequence of independent copies of a random vector &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; in &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$mathbb {R}^n$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. We revisit the question to determine the asymptotic shape of the random polytope &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;K&lt;/mi&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;conv&lt;/mi&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;mtext&gt;…&lt;/mtext&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;}&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$K_N={rm conv}lbrace X_1,ldots,X_Nrbrace$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;mo&gt;&gt;&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$N&gt;n$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. We show that for any &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;β&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$beta in (0,1)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; there exists a constant &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70665","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quasiconformal folding—a review of ‘Models for the Eremenko–Lyubich class'","authors":"Philip J. Rippon","doi":"10.1112/jlms.70662","DOIUrl":"https://doi.org/10.1112/jlms.70662","url":null,"abstract":"<p>We review the paper ‘Models for the Eremenko–Lyubich class’ by Bishop, which appeared in the Journal of the London Mathematical Society in 2015, the first of two LMS papers for which Bishop received the LMS Senior Berwick Prize in 2024. This is one of a series of papers where Bishop introduced his new technique of quasiconformal folding, which transformed the range of approaches to constructing examples of transcendental entire functions leading to the resolution of many open problems, in particular in transcendental dynamics.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70662","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Boolean compactness theorem for \u0000 \u0000 \u0000 L\u0000 \u0000 ∞\u0000 ∞\u0000 \u0000 \u0000 $mathrm{L}_{infty infty }$","authors":"Juan M. Santiago Suárez,&nbsp;Matteo Viale","doi":"10.1112/jlms.70654","DOIUrl":"https://doi.org/10.1112/jlms.70654","url":null,"abstract":"<p>We show that, contrary to the commonly held view, there is a natural and optimal compactness theorem for <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>L</mi>\u0000 <mrow>\u0000 <mi>∞</mi>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$mathrm{L}_{infty infty }$</annotation>\u0000 </semantics></math> which generalizes the usual compactness theorem for first-order logic. The key to this result is the switch from Tarski semantics to Boolean-valued semantics. On the way to prove it, we also show that the latter is a (the?) natural semantics both for <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>L</mi>\u0000 <mrow>\u0000 <mi>∞</mi>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$mathrm{L}_{infty infty }$</annotation>\u0000 </semantics></math> and for <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>L</mi>\u0000 <mrow>\u0000 <mi>∞</mi>\u0000 <mi>ω</mi>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$mathrm{L}_{infty omega }$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148752802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}