Inventiones mathematicae最新文献

{"title":"Coherent Springer theory and the categorical Deligne-Langlands correspondence","authors":"David Ben-Zvi, Harrison Chen, David Helm, David Nadler","doi":"10.1007/s00222-023-01224-2","DOIUrl":"https://doi.org/10.1007/s00222-023-01224-2","url":null,"abstract":"Abstract Kazhdan and Lusztig identified the affine Hecke algebra ℋ with an equivariant $K$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>K</mml:mi> </mml:math> -group of the Steinberg variety, and applied this to prove the Deligne-Langlands conjecture, i.e., the local Langlands parametrization of irreducible representations of reductive groups over nonarchimedean local fields $F$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>F</mml:mi> </mml:math> with an Iwahori-fixed vector. We apply techniques from derived algebraic geometry to pass from $K$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>K</mml:mi> </mml:math> -theory to Hochschild homology and thereby identify ℋ with the endomorphisms of a coherent sheaf on the stack of unipotent Langlands parameters, the coherent Springer sheaf . As a result the derived category of ℋ-modules is realized as a full subcategory of coherent sheaves on this stack, confirming expectations from strong forms of the local Langlands correspondence (including recent conjectures of Fargues-Scholze, Hellmann and Zhu). In the case of the general linear group our result allows us to lift the local Langlands classification of irreducible representations to a categorical statement: we construct a full embedding of the derived category of smooth representations of $mathrm{GL}_{n}(F)$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>GL</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo>(</mml:mo> <mml:mi>F</mml:mi> <mml:mo>)</mml:mo> </mml:math> into coherent sheaves on the stack of Langlands parameters.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135544860","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":"Localization crossover for the continuous Anderson Hamiltonian in 1-d","authors":"Laure Dumaz, Cyril Labbé","doi":"10.1007/s00222-023-01225-1","DOIUrl":"https://doi.org/10.1007/s00222-023-01225-1","url":null,"abstract":"We investigate the behavior of the spectrum of the continuous Anderson Hamiltonian $mathcal{H}_{L}$ , with white noise potential, on a segment whose size $L$ is sent to infinity. We zoom around energy levels $E$ either of order 1 (Bulk regime) or of order $1ll E ll L$ (Crossover regime). We show that the point process of (appropriately rescaled) eigenvalues and centers of mass converge to a Poisson point process. We also prove exponential localization of the eigenfunctions at an explicit rate. In addition, we show that the eigenfunctions converge to well-identified limits: in the Crossover regime, these limits are universal. Combined with the results of our companion paper (Dumaz and Labbé in Ann. Probab. 51(3):805–839, 2023), this identifies completely the transition between the localized and delocalized phases of the spectrum of $mathcal{H}_{L}$ . The two main technical challenges are the proof of a two-points or Minami estimate, as well as an estimate on the convergence to equilibrium of a hypoelliptic diffusion, the proof of which relies on Malliavin calculus and the theory of hypocoercivity.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135775117","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":"On the distribution of the Hodge locus","authors":"Gregorio Baldi, Bruno Klingler, Emmanuel Ullmo","doi":"10.1007/s00222-023-01226-0","DOIUrl":"https://doi.org/10.1007/s00222-023-01226-0","url":null,"abstract":"Abstract Given a polarizable ℤ-variation of Hodge structures $mathbb{V}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>V</mml:mi> </mml:math> over a complex smooth quasi-projective base $S$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>S</mml:mi> </mml:math> , a classical result of Cattani, Deligne and Kaplan says that its Hodge locus (i.e. the locus where exceptional Hodge tensors appear) is a countable union of irreducible algebraic subvarieties of $S$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>S</mml:mi> </mml:math> , called the special subvarieties for $mathbb{V}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>V</mml:mi> </mml:math> . Our main result in this paper is that, if the level of ${mathbb{V}}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>V</mml:mi> </mml:math> is at least 3, this Hodge locus is in fact a finite union of such special subvarieties (hence is algebraic), at least if we restrict ourselves to the Hodge locus factorwise of positive period dimension (Theorem 1.5). For instance the Hodge locus of positive period dimension of the universal family of degree $d$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>d</mml:mi> </mml:math> smooth hypersurfaces in $mathbf{P}^{n+1}_{mathbb{C}}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msubsup> <mml:mi>P</mml:mi> <mml:mi>C</mml:mi> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> , $ngeq 3$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>n</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>3</mml:mn> </mml:math> , $dgeq 5$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>d</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>5</mml:mn> </mml:math> and $(n,d)neq (4,5)$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>,</mml:mo> <mml:mi>d</mml:mi> <mml:mo>)</mml:mo> <mml:mo>≠</mml:mo> <mml:mo>(</mml:mo> <mml:mn>4</mml:mn> <mml:mo>,</mml:mo> <mml:mn>5</mml:mn> <mml:mo>)</mml:mo> </mml:math> , is algebraic. On the other hand we prove that in level 1 or 2, the Hodge locus is analytically dense in $S^{mbox{an}}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>S</mml:mi> <mml:mtext>an</mml:mtext> </mml:msup> </mml:math> as soon as it contains one typical special subvariety. These results follow from a complete elucidation of the distribution in $S$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>S</mml:mi> </mml:math> of the special subvarieties in terms of typical/atypical intersections, with the exception of the atypical special subvarieties of zero period dimension.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135775119","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":"Subgroups of hyperbolic groups, finiteness properties and complex hyperbolic lattices","authors":"Claudio Llosa Isenrich, Pierre Py","doi":"10.1007/s00222-023-01223-3","DOIUrl":"https://doi.org/10.1007/s00222-023-01223-3","url":null,"abstract":"Abstract We prove that in a cocompact complex hyperbolic arithmetic lattice $Gamma < {mathrm{PU}}(m,1)$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>Γ</mml:mi> <mml:mo><</mml:mo> <mml:mi>PU</mml:mi> <mml:mo>(</mml:mo> <mml:mi>m</mml:mi> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:math> of the simplest type, deep enough finite index subgroups admit plenty of homomorphisms to ℤ with kernel of type $mathscr{F}_{m-1}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>F</mml:mi> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> </mml:math> but not of type $mathscr{F}_{m}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>F</mml:mi> <mml:mi>m</mml:mi> </mml:msub> </mml:math> . This provides many finitely presented non-hyperbolic subgroups of hyperbolic groups and answers an old question of Brady. Our method also yields a proof of a special case of Singer’s conjecture for aspherical Kähler manifolds.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135923152","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 anisotropic Bernstein problem","authors":"Connor Mooney, Yang Yang","doi":"10.1007/s00222-023-01222-4","DOIUrl":"https://doi.org/10.1007/s00222-023-01222-4","url":null,"abstract":"Abstract We construct nonlinear entire anisotropic minimal graphs over $mathbb{R}^{4}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>4</mml:mn> </mml:msup> </mml:math> , completing the solution to the anisotropic Bernstein problem. The examples we construct have a variety of growth rates, and our approach both generalizes to higher dimensions and recovers and elucidates known examples of nonlinear entire minimal graphs over $mathbb{R}^{n},, n geq 8$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>R</mml:mi> <mml:mi>n</mml:mi> </mml:msup> <mml:mo>,</mml:mo> <mml:mspace /> <mml:mi>n</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>8</mml:mn> </mml:math> .","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135592232","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":"Character levels and character bounds for finite classical groups","authors":"Robert M. Guralnick, Michael Larsen, Pham Huu Tiep","doi":"10.1007/s00222-023-01221-5","DOIUrl":"https://doi.org/10.1007/s00222-023-01221-5","url":null,"abstract":"Abstract The main results of the paper develop a level theory and establish strong character bounds for finite classical groups, in the case that the centralizer of the element has small order compared to $|G|$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo>|</mml:mo> <mml:mi>G</mml:mi> <mml:mo>|</mml:mo> </mml:math> in a logarithmic sense.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135132129","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":"Nonuniformly elliptic Schauder theory","authors":"Cristiana De Filippis, Giuseppe Mingione","doi":"10.1007/s00222-023-01216-2","DOIUrl":"https://doi.org/10.1007/s00222-023-01216-2","url":null,"abstract":"Abstract Local Schauder theory holds in the nonuniformly elliptic setting. Specifically, first derivatives of solutions to nonuniformly elliptic problems are locally Hölder continuous if so are their coefficients.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135536574","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":"Non-reductive geometric invariant theory and hyperbolicity","authors":"Gergely Bérczi, Frances Kirwan","doi":"10.1007/s00222-023-01219-z","DOIUrl":"https://doi.org/10.1007/s00222-023-01219-z","url":null,"abstract":"Abstract The Green–Griffiths–Lang and Kobayashi hyperbolicity conjectures for generic hypersurfaces of polynomial degree are proved using intersection theory for non-reductive geometric invariant theoretic quotients and recent work of Riedl and Yang.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134904364","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":"On the birational section conjecture with strong birationality assumptions","authors":"Giulio Bresciani","doi":"10.1007/s00222-023-01220-6","DOIUrl":"https://doi.org/10.1007/s00222-023-01220-6","url":null,"abstract":"Abstract Let $X$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>X</mml:mi> </mml:math> be a curve over a field $k$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>k</mml:mi> </mml:math> finitely generated over ℚ and $t$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>t</mml:mi> </mml:math> an indeterminate. We prove that, if $s$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>s</mml:mi> </mml:math> is a section of $pi _{1}(X)to operatorname{Gal}(k)$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>π</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>)</mml:mo> <mml:mo>→</mml:mo> <mml:mo>Gal</mml:mo> <mml:mo>(</mml:mo> <mml:mi>k</mml:mi> <mml:mo>)</mml:mo> </mml:math> such that the base change $s_{k(t)}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>s</mml:mi> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:msub> </mml:math> is birationally liftable, then $s$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>s</mml:mi> </mml:math> comes from geometry. As a consequence we prove that the section conjecture is equivalent to the cuspidalization of all sections over all finitely generated fields.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134904248","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":"Moment maps and cohomology of non-reductive quotients","authors":"Gergely Bérczi, Frances Kirwan","doi":"10.1007/s00222-023-01218-0","DOIUrl":"https://doi.org/10.1007/s00222-023-01218-0","url":null,"abstract":"Abstract Let $H$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>H</mml:mi> </mml:math> be a complex linear algebraic group with internally graded unipotent radical acting on a complex projective variety $X$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>X</mml:mi> </mml:math> . Given an ample linearisation of the action and an associated Fubini–Study Kähler form which is invariant for a maximal compact subgroup $Q$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>Q</mml:mi> </mml:math> of $H$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>H</mml:mi> </mml:math> , we define a notion of moment map for the action of $H$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>H</mml:mi> </mml:math> , and under suitable conditions (that the linearisation is well-adapted and semistability coincides with stability) we describe the (non-reductive) GIT quotient $X/!/H$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>X</mml:mi> <mml:mo>/</mml:mo> <mml:mo>/</mml:mo> <mml:mi>H</mml:mi> </mml:math> introduced in (Bérczi et al. in J. Topol. 11(3):826–855, 2018) in terms of this moment map. Using this description we derive formulas for the Betti numbers of $X/!/H$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>X</mml:mi> <mml:mo>/</mml:mo> <mml:mo>/</mml:mo> <mml:mi>H</mml:mi> </mml:math> and express the rational cohomology ring of $X/!/H$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>X</mml:mi> <mml:mo>/</mml:mo> <mml:mo>/</mml:mo> <mml:mi>H</mml:mi> </mml:math> in terms of the rational cohomology ring of the GIT quotient $X/!/T^{H}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>X</mml:mi> <mml:mo>/</mml:mo> <mml:mo>/</mml:mo> <mml:msup> <mml:mi>T</mml:mi> <mml:mi>H</mml:mi> </mml:msup> </mml:math> , where $T^{H}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>T</mml:mi> <mml:mi>H</mml:mi> </mml:msup> </mml:math> is a maximal torus in $H$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>H</mml:mi> </mml:math> . We relate intersection pairings on $X/!/H$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>X</mml:mi> <mml:mo>/</mml:mo> <mml:mo>/</mml:mo> <mml:mi>H</mml:mi> </mml:math> to intersection pairings on $X/!/T^{H}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>X</mml:mi> <mml:mo>/</mml:mo> <mml:mo>/</mml:mo> <mml:msup> <mml:mi>T</mml:mi> <mml:mi>H</mml:mi> </mml:msup> </mml:math> , obtaining a residue formula for these pairings on $X/!/H$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>X</mml:mi> <mml:mo>/</mml:mo> <mml:mo>/</mml:mo> <mml:mi>H</mml:mi> </mml:math> analogous to the residue formula of (Jeffrey and Kirwan in Topology 34(2):291–327, 1995). As an application, we announce a proof of the Green–Griffiths–Lang and Kobayashi conjectures for projective hypersurfaces with polynomial degree.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134904363","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}