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

{"title":"On tamely ramified infinite Galois extensions","authors":"Farshid Hajir, Michael Larsen, Christian Maire, Ravi Ramakrishna","doi":"10.1112/jlms.70209","DOIUrl":"10.1112/jlms.70209","url":null,"abstract":"<p>For a number field <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math>, we consider <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>K</mi>\u0000 <mi>ta</mi>\u0000 </msup>\u0000 <annotation>$K^{{rm ta}}$</annotation>\u0000 </semantics></math> the maximal tamely ramified algebraic extension of <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math>, and its Galois group <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>G</mi>\u0000 <mi>K</mi>\u0000 <mi>ta</mi>\u0000 </msubsup>\u0000 <mo>=</mo>\u0000 <mi>Gal</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>K</mi>\u0000 <mi>ta</mi>\u0000 </msup>\u0000 <mo>/</mo>\u0000 <mi>K</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$G^{{rm ta}}_K= mathrm{Gal}(K^{{rm ta}}/K)$</annotation>\u0000 </semantics></math>. Choose an odd prime <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>. Our guiding aim is to characterize the finitely generated pro-<span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math> quotients of <span></span><math>\u0000 <semantics>\u0000 <msubsup>\u0000 <mi>G</mi>\u0000 <mi>K</mi>\u0000 <mi>ta</mi>\u0000 </msubsup>\u0000 <annotation>$G^{{rm ta}}_K$</annotation>\u0000 </semantics></math>. We give a unified point of view by introducing the notion of <i>stably inertially generated</i> pro-<span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math> groups <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>, for which linear groups are archetypes. This key notion is compatible with local <i>tame liftings</i> as used in the Scholz–Reichardt theorem. We realize every finitely generated pro-<span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math> group <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> which is stably inertially generated as a quotient of <span></span><math>\u0000 <semantics>\u0000","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144520310","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":"Weak compactness cardinals for strong logics and subtlety properties of the class of ordinals","authors":"Philipp Lücke","doi":"10.1112/jlms.70215","DOIUrl":"10.1112/jlms.70215","url":null,"abstract":"<p>Motivated by recent work of Boney, Dimopoulos, Gitman, and Magidor, we characterize the existence of weak compactness cardinals for all abstract logics through combinatorial properties of the class of ordinals. This analysis is then used to show that, in contrast to the existence of strong compactness cardinals, the existence of weak compactness cardinals for abstract logics does not imply the existence of a strongly inaccessible cardinal. More precisely, it is proven that the existence of a proper class of subtle cardinals is consistent with the axioms of <span></span><math>\u0000 <semantics>\u0000 <mi>ZFC</mi>\u0000 <annotation>${rm {ZFC}}$</annotation>\u0000 </semantics></math> if and only if it is not possible to derive the existence of strongly inaccessible cardinals from the existence of weak compactness cardinals for all abstract logics. Complementing this result, it is shown that the existence of weak compactness cardinals for all abstract logics implies that unboundedly many ordinals are strongly inaccessible in the inner model <span></span><math>\u0000 <semantics>\u0000 <mi>HOD</mi>\u0000 <annotation>${rm {HOD}}$</annotation>\u0000 </semantics></math> of all hereditarily ordinal definable sets.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70215","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144519647","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":"Equivariant geometry of singular cubic threefolds, II","authors":"Ivan Cheltsov,&nbsp;Lisa Marquand,&nbsp;Yuri Tschinkel,&nbsp;Zhijia Zhang","doi":"10.1112/jlms.70224","DOIUrl":"10.1112/jlms.70224","url":null,"abstract":"<p>We study linearizability of actions of finite groups on cubic threefolds with nonnodal isolated singularities.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70224","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144520311","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":"Modularity of \u0000 \u0000 d\u0000 $d$\u0000 -elliptic loci with level structure","authors":"François Greer,&nbsp;Carl Lian","doi":"10.1112/jlms.70212","DOIUrl":"10.1112/jlms.70212","url":null,"abstract":"<p>We consider the generating series of special cycles on <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>A</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>N</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>×</mo>\u0000 <msub>\u0000 <mi>A</mi>\u0000 <mi>g</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>N</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathcal {A}_1(N)times mathcal {A}_g(N)$</annotation>\u0000 </semantics></math>, with full level <span></span><math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$N$</annotation>\u0000 </semantics></math> structure, valued in the cohomology of degree <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>g</mi>\u0000 </mrow>\u0000 <annotation>$2g$</annotation>\u0000 </semantics></math>. The modularity theorem of Kudla–Millson for locally symmetric spaces implies that these series are modular. When <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>=</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$N=1$</annotation>\u0000 </semantics></math>, the images of these loci in <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>A</mi>\u0000 <mi>g</mi>\u0000 </msub>\u0000 <annotation>$mathcal {A}_g$</annotation>\u0000 </semantics></math> are the <span></span><math>\u0000 <semantics>\u0000 <mi>d</mi>\u0000 <annotation>$d$</annotation>\u0000 </semantics></math>-elliptic Noether–Lefschetz loci, which are conjectured to be modular. In the Appendix, it is shown that the resulting modular forms are nonzero for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>g</mi>\u0000 <mo>=</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$g=2$</annotation>\u0000 </semantics></math> when <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>⩾</mo>\u0000 <mn>11</mn>\u0000 </mrow>\u0000 <annotation>$Ngeqslant 11$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>≠</mo>\u0000 <mn>12</mn>\u0000 </mrow>\u0000 <annotation>$Nne 12$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144473187","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":"Moduli of finite flat torsors over nodal curves","authors":"Sara Mehidi,&nbsp;Thibault Poiret","doi":"10.1112/jlms.70220","DOIUrl":"10.1112/jlms.70220","url":null,"abstract":"<p>We show that log flat torsors over a family <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>X</mi>\u0000 <mo>/</mo>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 <annotation>$X/S$</annotation>\u0000 </semantics></math> of nodal curves under a finite flat commutative group scheme <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 <mo>/</mo>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 <annotation>$G/S$</annotation>\u0000 </semantics></math> are classified by maps from the Cartier dual of <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> to the log Jacobian of <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math>. We deduce that fppf torsors on the smooth fiberss of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>X</mi>\u0000 <mo>/</mo>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 <annotation>$X/S$</annotation>\u0000 </semantics></math> can be extended to global log flat torsors under some regularity hypotheses.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70220","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144473185","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":"Locally primitive block designs","authors":"Jianfu Chen,&nbsp;Peice Hua,&nbsp;Cai Heng Li,&nbsp;Yanni Wu","doi":"10.1112/jlms.70221","DOIUrl":"10.1112/jlms.70221","url":null,"abstract":"<p>A locally primitive 2-design is a 2-design admitting an automorphism group <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> with primitive local actions. It is proved that <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> is point-primitive, and either <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> is an almost simple group, or <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> acts on the points as an affine group.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144473072","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":"Continuity of HYM connections with respect to metric variations","authors":"Rémi Delloque","doi":"10.1112/jlms.70219","DOIUrl":"10.1112/jlms.70219","url":null,"abstract":"<p>We investigate the set of (real Dolbeault classes of) balanced metrics <span></span><math>\u0000 <semantics>\u0000 <mi>Θ</mi>\u0000 <annotation>$Theta$</annotation>\u0000 </semantics></math> on a balanced manifold <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> with respect to which a torsion-free coherent sheaf <span></span><math>\u0000 <semantics>\u0000 <mi>E</mi>\u0000 <annotation>$mathcal {E}$</annotation>\u0000 </semantics></math> on <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> is slope stable. We prove that the set of all such <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 <mi>Θ</mi>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <mo>∈</mo>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>X</mi>\u0000 <mo>,</mo>\u0000 <mi>R</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$[Theta] in H^{n - 1,n - 1}(X,mathbb {R})$</annotation>\u0000 </semantics></math> is an open convex cone locally defined by a finite number of linear inequalities. When <span></span><math>\u0000 <semantics>\u0000 <mi>E</mi>\u0000 <annotation>$mathcal {E}$</annotation>\u0000 </semantics></math> is a Hermitian vector bundle, the Kobayashi–Hitchin correspondence provides associated Hermitian Yang–Mills connections, which we show depend continuously on the metric, even around classes with respect to which <span></span><math>\u0000 <semantics>\u0000 <mi>E</mi>\u0000 <annotation>$mathcal {E}$</annotation>\u0000 </semantics></math> is only semi-stable. In this case, the holomorphic structure induced by the connection is the holomorphic structure of the associated graded object. The method relies on semi-stable perturbation techniques for geometric PDEs with a moment map interpretation and is quite versatile, and we hope that it can be used in other similar problems.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70219","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144473184","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 fundamental group and the magnitude-path spectral sequence of a directed graph","authors":"Daisuke Kishimoto,&nbsp;Yichen Tong","doi":"10.1112/jlms.70210","DOIUrl":"10.1112/jlms.70210","url":null,"abstract":"<p>The fundamental group of a directed graph admits a natural sequence of quotient groups called <span></span><math>\u0000 <semantics>\u0000 <mi>r</mi>\u0000 <annotation>$r$</annotation>\u0000 </semantics></math>-fundamental groups, and the <span></span><math>\u0000 <semantics>\u0000 <mi>r</mi>\u0000 <annotation>$r$</annotation>\u0000 </semantics></math>-fundamental groups can capture properties of a directed graph that the fundamental group cannot capture. The fundamental group of a directed graph is related to path homology through the Hurewicz theorem. The magnitude-path spectral sequence connects magnitude homology and path homology of a directed graph, and it may be thought of as a sequence of homology of a directed graph, including path homology. In this paper, we study relations of the <span></span><math>\u0000 <semantics>\u0000 <mi>r</mi>\u0000 <annotation>$r$</annotation>\u0000 </semantics></math>-fundamental groups and the magnitude-path spectral sequence through the Hurewicz theorem and the Seifert–van Kampen theorem.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144473071","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 simple construction of the sine-Gordon model via stochastic quantization","authors":"Massimiliano Gubinelli,&nbsp;Martin Hairer,&nbsp;Tadahiro Oh,&nbsp;Younes Zine","doi":"10.1112/jlms.70214","DOIUrl":"10.1112/jlms.70214","url":null,"abstract":"<p>We present a simple PDE construction of the sine-Gordon measure below the first threshold (<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>β</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>&lt;</mo>\u0000 <mn>4</mn>\u0000 <mi>π</mi>\u0000 </mrow>\u0000 <annotation>$beta ^2 &lt; 4pi$</annotation>\u0000 </semantics></math>), in both the finite and infinite volume settings, by studying the corresponding parabolic sine-Gordon model. We also establish pathwise global well-posedness of the hyperbolic sine-Gordon model in finite volume for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>β</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>&lt;</mo>\u0000 <mn>2</mn>\u0000 <mi>π</mi>\u0000 </mrow>\u0000 <annotation>$beta ^2 &lt; 2pi$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70214","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144473186","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":"Corrigendum to “Relatively geometric actions on CAT(0) cube complexes”","authors":"Eduard Einstein,&nbsp;Daniel Groves","doi":"10.1112/jlms.70211","DOIUrl":"10.1112/jlms.70211","url":null,"abstract":"<p>We identify an error in E. Einstein and D. Groves [J. Lond. Math. Soc. (2), <b>105</b> (2022), no. 1, 691–708] which affects the construction of a completion and retraction of complexes of groups.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 6","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70211","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144315312","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}