Advances in Mathematics最新文献

{"title":"Asymptotic behavior of complete conformal metric near singular boundary","authors":"Weiming Shen,&nbsp;Yue Wang","doi":"10.1016/j.aim.2024.109977","DOIUrl":"10.1016/j.aim.2024.109977","url":null,"abstract":"<div><div>The boundary behavior of the singular Yamabe problem has been extensively studied near sufficiently smooth boundaries, while less is known about the asymptotic behavior of solutions near singular boundaries. In this paper, we study the asymptotic behaviors of solutions to the singular Yamabe problem with negative constant scalar curvature near singular boundaries and derive the optimal estimates for the background metric which is not necessarily conformally flat. In particular, we prove that the solutions are well approximated by the solutions in tangent cones at singular points on the boundaries.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"458 ","pages":"Article 109977"},"PeriodicalIF":1.5,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Milnor-Witt motivic cohomology and linear algebraic groups","authors":"Keyao Peng","doi":"10.1016/j.aim.2024.109973","DOIUrl":"10.1016/j.aim.2024.109973","url":null,"abstract":"<div><div>This article presents two key computations in MW-motivic cohomology. Firstly, we compute the MW-motivic cohomology of the symplectic groups <span><math><msub><mrow><mi>Sp</mi></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msub></math></span> for any <span><math><mi>n</mi><mo>∈</mo><mi>N</mi></math></span> using the Sp-orientation and the associated Borel classes.</div><div>Secondly, following the classical computations and using the analogue in <span><math><msup><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-homotopy of the Leray spectral sequence, we compute the <em>η</em>-inverted MW-motivic cohomology of general Stiefel varieties, obtaining in particular the computation of the <em>η</em>-inverted MW-motivic cohomology of the general linear groups <span><math><msub><mrow><mi>GL</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> and the special linear groups <span><math><msub><mrow><mi>SL</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> for any <span><math><mi>n</mi><mo>∈</mo><mi>N</mi></math></span>.</div><div>Finally, we determine the multiplicative structures of these total cohomology groups.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"458 ","pages":"Article 109973"},"PeriodicalIF":1.5,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Shuffle algebras, lattice paths and Macdonald functions","authors":"Alexandr Garbali,&nbsp;Ajeeth Gunna","doi":"10.1016/j.aim.2024.109974","DOIUrl":"10.1016/j.aim.2024.109974","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We consider partition functions on the &lt;span&gt;&lt;math&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; square lattice with the local Boltzmann weights given by the &lt;em&gt;R&lt;/em&gt;-matrix of the &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;U&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ˆ&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; quantum algebra. We identify boundary states such that the square lattice can be viewed on a conic surface. The partition function &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; on this lattice computes the weighted sum over all possible closed coloured lattice paths with &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; different colours: &lt;em&gt;n&lt;/em&gt; “bosonic” colours and &lt;em&gt;m&lt;/em&gt; “fermionic” colours. Each bosonic (fermionic) path of colour &lt;em&gt;i&lt;/em&gt; contributes a factor of &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; (&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;) to the weight of the configuration. We show the following:&lt;ul&gt;&lt;li&gt;&lt;span&gt;i)&lt;/span&gt;&lt;span&gt;&lt;div&gt;&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is a symmetric function in the spectral parameters &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;…&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and generates basis elements of the commutative trigonometric Feigin–Odesskii shuffle algebra. The generating function of &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; admits a shuffle-exponential formula analogous to the Macdonald Cauchy kernel.&lt;/div&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span&gt;ii)&lt;/span&gt;&lt;span&gt;&lt;div&gt;&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is a symmetric function in two alphabets &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;…&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;…&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. When &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;…&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; are set to be equal to the box content of a skew Young diagram &lt;span&gt;&lt;math&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; with &lt;em&gt;N&lt;/em&gt; boxes the partition function &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; reproduces the skew Macdonald function &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;.&lt;/div&gt;&lt;/span&gt;&lt;/li&gt;&lt;/","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"458 ","pages":"Article 109974"},"PeriodicalIF":1.5,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stability of Llarull's theorem in all dimensions","authors":"Sven Hirsch ,&nbsp;Yiyue Zhang","doi":"10.1016/j.aim.2024.109980","DOIUrl":"10.1016/j.aim.2024.109980","url":null,"abstract":"<div><div>Llarull's theorem characterizes the round sphere <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> among all spin manifolds whose scalar curvature is bounded from below by <span><math><mi>n</mi><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span>. In this paper we show that if the scalar curvature is bounded from below by <span><math><mi>n</mi><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>−</mo><mi>ε</mi></math></span>, the underlying manifold is <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span>-close to a finite number of spheres outside a small bad set. This completely solves Gromov's spherical stability problem and is the first instance of a scalar curvature stability result that both holds in all dimensions and is stated without any additional geometrical or topological assumptions.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"458 ","pages":"Article 109980"},"PeriodicalIF":1.5,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532269","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Generalized cohomology theories for algebraic stacks","authors":"Adeel A. Khan ,&nbsp;Charanya Ravi","doi":"10.1016/j.aim.2024.109975","DOIUrl":"10.1016/j.aim.2024.109975","url":null,"abstract":"<div><div>We extend the stable motivic homotopy category of Voevodsky to the class of scalloped algebraic stacks, and show that it admits the formalism of Grothendieck's six operations. Objects in this category represent generalized cohomology theories for stacks like algebraic K-theory, as well as new examples like genuine motivic cohomology and algebraic cobordism. These cohomology theories admit Gysin maps and satisfy homotopy invariance, localization, and Mayer–Vietoris. For example, we deduce that homotopy K-theory satisfies cdh descent on scalloped stacks. We also prove a fixed point localization formula for torus actions.</div><div>Finally, the construction is contrasted with a “lisse-extended” stable motivic homotopy category, defined for arbitrary stacks: we show for example that lisse-extended motivic cohomology of quotient stacks is computed by the equivariant higher Chow groups of Edidin–Graham, and we also get a good new theory of Borel-equivariant algebraic cobordism. Moreover, the lisse-extended motivic homotopy type is shown to recover all previous constructions of motives of stacks.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"458 ","pages":"Article 109975"},"PeriodicalIF":1.5,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Duality for weak multiplier Hopf algebras with sufficiently many integrals","authors":"Alfons Van Daele ,&nbsp;Shuanhong Wang","doi":"10.1016/j.aim.2024.109971","DOIUrl":"10.1016/j.aim.2024.109971","url":null,"abstract":"<div><div>We study duality of regular weak multiplier Hopf algebras with sufficiently many integrals. This generalizes the well-known duality of algebraic quantum groups. We need to modify the definition of an integral in this case. It is no longer true that an integral is automatically faithful and unique. Therefore we have to work with a faithful set of integrals. We apply the theory to three cases and give some examples. First we have the two weak multiplier Hopf algebras associated with an infinite groupoid (a small category). Related we answer a question posed by Nicolás Andruskiewitsch about double groupoids. Finally, we also discuss the weak multiplier Hopf algebras associated to a separability idempotent.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"458 ","pages":"Article 109971"},"PeriodicalIF":1.5,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Koebe conjecture and the Weyl problem for convex surfaces in hyperbolic 3-space","authors":"Feng Luo ,&nbsp;Tianqi Wu","doi":"10.1016/j.aim.2024.109969","DOIUrl":"10.1016/j.aim.2024.109969","url":null,"abstract":"<div><div>We prove that the Koebe circle domain conjecture is equivalent to the Weyl type problem that every complete hyperbolic surface of genus zero is isometric to the boundary of the hyperbolic convex hull of the complement of a circle domain in the hyperbolic 3-space. Applications of the result to discrete conformal geometry will be discussed. The main tool we use is Schramm's transboundary extremal lengths.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"458 ","pages":"Article 109969"},"PeriodicalIF":1.5,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bounding projective hypersurface singularities","authors":"Ben Castor","doi":"10.1016/j.aim.2024.109970","DOIUrl":"10.1016/j.aim.2024.109970","url":null,"abstract":"<div><div>We compare several different methods involving Hodge-theoretic spectra of singularities which produce constraints on the number and type of isolated singularities on a projective hypersurface of fixed degree. In particular, we introduce a method based on the spectrum of the nonisolated singularity at the origin of the affine cone on such a hypersurface, and relate the resulting explicit formula to Varchenko's bound.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"458 ","pages":"Article 109970"},"PeriodicalIF":1.5,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Higher Chow groups with finite coefficients and refined unramified cohomology","authors":"Kees Kok ,&nbsp;Lin Zhou","doi":"10.1016/j.aim.2024.109972","DOIUrl":"10.1016/j.aim.2024.109972","url":null,"abstract":"<div><div>In this paper we show that Bloch's higher cycle class map with finite coefficients for quasi-projective equi-dimensional schemes over a field fits naturally in a long exact sequence involving Schreieder's refined unramified cohomology. We also show that the refined unramified cohomology satisfies the localization sequence. Using this we conjecture in the end that refined unramified cohomology is a motivic homology theory and explain how this is related to the aforementioned results.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"458 ","pages":"Article 109972"},"PeriodicalIF":1.5,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Blow-up invariance of cohomology theories with modulus","authors":"Junnosuke Koizumi","doi":"10.1016/j.aim.2024.109967","DOIUrl":"10.1016/j.aim.2024.109967","url":null,"abstract":"<div><div>In this paper, we study cohomology theories of <span><math><mi>Q</mi></math></span>-modulus pairs, which are pairs <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>D</mi><mo>)</mo></math></span> consisting of a scheme <em>X</em> and a <span><math><mi>Q</mi></math></span>-divisor <em>D</em>. Our main theorem provides a sufficient condition for such a cohomology theory to be invariant under blow-ups with centers contained in the divisor. This yields a short proof of the blow-up invariance of the Hodge cohomology with modulus proved by Kelly-Miyazaki. We also define the Witt vector cohomology with modulus using the Brylinski-Kato filtration and prove its blow-up invariance.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"458 ","pages":"Article 109967"},"PeriodicalIF":1.5,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}