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Ax–Schanuel for variations of mixed Hodge structures 混合霍奇结构变化的 Ax-Schanuel
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-10 DOI: 10.1007/s00208-024-02958-x
Kenneth Chung Tak Chiu
{"title":"Ax–Schanuel for variations of mixed Hodge structures","authors":"Kenneth Chung Tak Chiu","doi":"10.1007/s00208-024-02958-x","DOIUrl":"https://doi.org/10.1007/s00208-024-02958-x","url":null,"abstract":"<p>We give properties of the real-split retraction of the mixed weak Mumford–Tate domain and prove the Ax–Schanuel property of period mappings arising from variations of mixed Hodge structures. An ingredient in the proof is the definability of the mixed period mapping obtained by Bakker–Brunebarbe–Klingler–Tsimerman. In comparison with preceding results, in the point counting step, we count rational points on definable quotients instead.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"80 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141940005","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}
引用次数: 0
Specialization maps for Scholze’s category of diamonds 舒尔茨钻石类别的特化图
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-08 DOI: 10.1007/s00208-024-02952-3
Ian Gleason
{"title":"Specialization maps for Scholze’s category of diamonds","authors":"Ian Gleason","doi":"10.1007/s00208-024-02952-3","DOIUrl":"https://doi.org/10.1007/s00208-024-02952-3","url":null,"abstract":"<p>We introduce the specialization map in Scholze’s theory of diamonds. We consider v-sheaves that “behave like formal schemes\" and call them kimberlites. We attach to them: a reduced special fiber, an analytic locus, a specialization map, a Zariski site, and an étale site. When the kimberlite comes from a formal scheme, our sites recover the classical ones. We prove that unramified <i>p</i>-adic Beilinson–Drinfeld Grassmannians are kimberlites with finiteness and normality properties.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"41 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141940128","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}
引用次数: 0
Monogamy of entanglement between cones 锥体间纠缠的一夫一妻制
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-07 DOI: 10.1007/s00208-024-02935-4
Guillaume Aubrun, Alexander Müller-Hermes, Martin Plávala
{"title":"Monogamy of entanglement between cones","authors":"Guillaume Aubrun, Alexander Müller-Hermes, Martin Plávala","doi":"10.1007/s00208-024-02935-4","DOIUrl":"https://doi.org/10.1007/s00208-024-02935-4","url":null,"abstract":"<p>A separable quantum state shared between parties <i>A</i> and <i>B</i> can be symmetrically extended to a quantum state shared between party <i>A</i> and parties <span>(B_1,ldots ,B_k)</span> for every <span>(kin textbf{N})</span>. Quantum states that are not separable, i.e., entangled, do not have this property. This phenomenon is known as “monogamy of entanglement”. We show that monogamy is not only a feature of quantum theory, but that it characterizes the minimal tensor product of general pairs of convex cones <span>(textsf{C}_A)</span> and <span>(textsf{C}_B)</span>: The elements of the minimal tensor product <span>(textsf{C}_Aotimes _{min } textsf{C}_B)</span> are precisely the tensors that can be symmetrically extended to elements in the maximal tensor product <span>(textsf{C}_Aotimes _{max } textsf{C}^{otimes _{max } k}_B)</span> for every <span>(kin textbf{N})</span>. Equivalently, the minimal tensor product of two cones is the intersection of the nested sets of <i>k</i>-extendible tensors. It is a natural question when the minimal tensor product <span>(textsf{C}_Aotimes _{min } textsf{C}_B)</span> coincides with the set of <i>k</i>-extendible tensors for some finite <i>k</i>. We show that this is universally the case for every cone <span>(textsf{C}_A)</span> if and only if <span>(textsf{C}_B)</span> is a polyhedral cone with a base given by a product of simplices. Our proof makes use of a new characterization of products of simplices up to affine equivalence that we believe is of independent interest.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"311 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141940007","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}
引用次数: 0
Calibrated representations of the double Dyck path algebra 双戴克路径代数的校准表示法
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-06 DOI: 10.1007/s00208-024-02937-2
Nicolle González, Eugene Gorsky, José Simental
{"title":"Calibrated representations of the double Dyck path algebra","authors":"Nicolle González, Eugene Gorsky, José Simental","doi":"10.1007/s00208-024-02937-2","DOIUrl":"https://doi.org/10.1007/s00208-024-02937-2","url":null,"abstract":"<p>The double Dyck path algebra <span>(mathbb {A}_{q,t})</span> and its polynomial representation first arose as a key figure in the proof of the celebrated Shuffle Theorem of Carlsson and Mellit. A geometric formulation for an equivalent algebra <span>(mathbb {B}_{q,t})</span> was then given by the second author and Carlsson and Mellit using the K-theory of parabolic flag Hilbert schemes. In this article, we initiate the systematic study of the representation theory of the double Dyck path algebra <span>(mathbb {B}_{q,t})</span>. We define a natural extension of this algebra and study its calibrated representations. We show that the polynomial representation is calibrated, and place it into a large family of calibrated representations constructed from posets satisfying certain conditions. We also define tensor products and duals of these representations, thus proving (under suitable conditions) the category of calibrated representations is generically monoidal. As an application, we prove that tensor powers of the polynomial representation can be constructed from the equivariant K-theory of parabolic Gieseker moduli spaces.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"43 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141940008","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}
引用次数: 0
The isoperimetric problem in the Riemannian manifold admitting a non-trivial conformal vector field 容纳非三维共形向量场的黎曼流形中的等周问题
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-03 DOI: 10.1007/s00208-024-02954-1
Jiayu Li, Shujing Pan
{"title":"The isoperimetric problem in the Riemannian manifold admitting a non-trivial conformal vector field","authors":"Jiayu Li, Shujing Pan","doi":"10.1007/s00208-024-02954-1","DOIUrl":"https://doi.org/10.1007/s00208-024-02954-1","url":null,"abstract":"<p>In this article, we will study the isoperimetric problem by introducing a mean curvature type flow in the Riemannian manifold endowed with a non-trivial conformal vector field. This flow preserves the volume of the bounded domain enclosed by a star-shaped hypersurface and decreases the area of hypersurface under certain conditions. We will prove the long time existence and convergence of the flow. As a result, the isoperimetric inequality for such a domain is established. Especially, we solve the isoperimetric problem for the star-shaped hypersurfaces in the Riemannian manifold endowed with a closed, non-trivial conformal vector field, a wide class of warped product spaces studied by Guan, Li and Wang is included.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"75 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141880496","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}
引用次数: 0
Resolvent estimates for the Stokes operator in bounded and exterior $$C^1$$ domains 斯托克斯算子在有界和外部 $$C^1$$ 域中的残差估计值
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-03 DOI: 10.1007/s00208-024-02956-z
Jun Geng, Zhongwei Shen
{"title":"Resolvent estimates for the Stokes operator in bounded and exterior $$C^1$$ domains","authors":"Jun Geng, Zhongwei Shen","doi":"10.1007/s00208-024-02956-z","DOIUrl":"https://doi.org/10.1007/s00208-024-02956-z","url":null,"abstract":"<p>We establish resolvent estimates in <span>(L^q)</span> spaces for the Stokes operator in a bounded <span>(C^1)</span> domain <span>(Omega )</span> in <span>(mathbb {R}^{d})</span>. As a corollary, it follows that the Stokes operator generates a bounded analytic semigroup in <span>(L^q(Omega ; mathbb {C}^d))</span> for any <span>(1&lt; q&lt; infty )</span> and <span>(dge 2)</span>. The case of an exterior <span>(C^1)</span> domain is also studied.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"222 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886765","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}
引用次数: 0
The regularity of difference divisors 差分除法的规律性
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-07-30 DOI: 10.1007/s00208-024-02950-5
Baiqing Zhu
{"title":"The regularity of difference divisors","authors":"Baiqing Zhu","doi":"10.1007/s00208-024-02950-5","DOIUrl":"https://doi.org/10.1007/s00208-024-02950-5","url":null,"abstract":"<p>For a prime number <span>(p&gt;2)</span> and a finite extension <span>(F/mathbb {Q}_p)</span>, we explain the construction of the difference divisors on the unitary Rapoport–Zink spaces of hyperspecial level over <span>(mathcal {O}_{breve{F}})</span>, and the GSpin Rapoport–Zink spaces of hyperspecial level over <span>(breve{mathbb {Z}}_{p})</span> associated to a minuscule cocharacter <span>(mu )</span> and a basic element <i>b</i>. We prove the regularity of the difference divisors, find the formally smooth locus of both the special cycles and the difference divisors, by a purely deformation-theoretic approach.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"108 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872581","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}
引用次数: 0
Newton polygons of sums on curves I: local-to-global theorems 曲线上和的牛顿多边形 I：局部到全局定理
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-07-29 DOI: 10.1007/s00208-024-02949-y
Joe Kramer-Miller, James Upton
{"title":"Newton polygons of sums on curves I: local-to-global theorems","authors":"Joe Kramer-Miller, James Upton","doi":"10.1007/s00208-024-02949-y","DOIUrl":"https://doi.org/10.1007/s00208-024-02949-y","url":null,"abstract":"<p>The purpose of this article is to study Newton polygons of certain abelian <i>L</i>-functions on curves. Let <i>X</i> be a smooth affine curve over a finite field <span>(mathbb {F}_q)</span> and let <span>(rho :pi _1(X) rightarrow mathbb {C}_p^times )</span> be a finite character of order <span>(p^n)</span>. By previous work of the first author, the Newton polygon <span>({{,mathrm{text {NP}},}}(rho ))</span> lies above a ‘Hodge polygon’ <span>({{,mathrm{text {HP}},}}(rho ))</span> defined using ramification invariants of <span>(rho )</span>. In this article we study the contact between these two polygons. We prove that <span>({{,mathrm{text {NP}},}}(rho ))</span> and <span>({{,mathrm{text {HP}},}}(rho ))</span> share a vertex if and only if a corresponding vertex is shared between the Newton and Hodge polygons of ‘local’ <i>L</i>-functions associated to each ramified point of <span>(rho )</span>. As a consequence, we determine a necessary and sufficient condition for the coincidence of <span>({{,mathrm{text {NP}},}}(rho ))</span> and <span>({{,mathrm{text {HP}},}}(rho ))</span>.\u0000</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"29 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872582","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}
引用次数: 0
Compact Kähler three-folds with nef anti-canonical bundle 具有 nef 反典型束的紧凑凯勒三折叠
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-07-28 DOI: 10.1007/s00208-024-02934-5
Shin-ichi Matsumura, Xiaojun Wu
{"title":"Compact Kähler three-folds with nef anti-canonical bundle","authors":"Shin-ichi Matsumura, Xiaojun Wu","doi":"10.1007/s00208-024-02934-5","DOIUrl":"https://doi.org/10.1007/s00208-024-02934-5","url":null,"abstract":"<p>In this paper, we prove that a non-projective compact Kähler three-fold with nef anti-canonical bundle is, up to a finite étale cover, one of the following: a manifold with vanishing first Chern class; the product of a K3 surface and the projective line; or a projective space bundle over a two-dimensional torus. This result extends Cao–Höring’s structure theorem for projective manifolds to compact Kähler manifolds in dimension 3. For the proof, we investigate the Minimal Model Program for compact Kähler three-folds with nef anti-canonical bundles by using the positivity of direct image sheaves, <span>(mathbb {Q})</span>-conic bundles, and orbifold vector bundles.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"39 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775636","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}
引用次数: 0
Regularity results for quasiminima of a class of double phase problems 一类双相问题准极限的正则性结果
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-07-23 DOI: 10.1007/s00208-024-02947-0
Antonella Nastasi, Cintia Pacchiano Camacho
{"title":"Regularity results for quasiminima of a class of double phase problems","authors":"Antonella Nastasi, Cintia Pacchiano Camacho","doi":"10.1007/s00208-024-02947-0","DOIUrl":"https://doi.org/10.1007/s00208-024-02947-0","url":null,"abstract":"<p>We prove boundedness, Hölder continuity, Harnack inequality results for local quasiminima to elliptic double phase problems of <i>p</i>-Laplace type in the general context of metric measure spaces. The proofs follow a variational approach and they are based on the De Giorgi method, a careful phase analysis and estimates in the intrinsic geometries.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"18 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775637","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}
引用次数: 0
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