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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 Q1 MATHEMATICS Pub Date : 2024-08-10 DOI: 10.1007/s00208-024-02958-x
Kenneth Chung Tak Chiu

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.

我们给出了混合弱 Mumford-Tate 域的实分裂回缩的性质,并证明了由混合霍奇结构的变化所产生的周期映射的 Ax-Schanuel 性质。证明的一个要素是巴克尔-布鲁内巴伯-克林勒-齐默尔曼(Bakker-Brunebarbe-Klingler-Tsimerman)所得到的混合周期映射的可定义性。与之前的结果相比,在计算点的步骤中,我们计算的是可定义商上的有理点。
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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 Q1 MATHEMATICS Pub Date : 2024-08-08 DOI: 10.1007/s00208-024-02952-3
Ian Gleason

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 p-adic Beilinson–Drinfeld Grassmannians are kimberlites with finiteness and normality properties.

我们介绍舒尔茨钻石理论中的特化映射。我们考虑了 "表现得像形式方案 "的 v 谢弗,并称它们为金伯利特。我们给它们附加了:还原特殊纤维、解析位置、特化映射、扎里斯基位置和埃塔莱位置。当金伯利岩来自形式方案时,我们的位点就恢复了经典位点。我们证明了非ramified p-adic Beilinson-Drinfeld Grassmannians 是具有有限性和规范性的金伯利特。
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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 Q1 MATHEMATICS Pub Date : 2024-08-07 DOI: 10.1007/s00208-024-02935-4
Guillaume Aubrun, Alexander Müller-Hermes, Martin Plávala

A separable quantum state shared between parties A and B can be symmetrically extended to a quantum state shared between party A and parties (B_1,ldots ,B_k) for every (kin textbf{N}). 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 (textsf{C}_A) and (textsf{C}_B): The elements of the minimal tensor product (textsf{C}_Aotimes _{min } textsf{C}_B) are precisely the tensors that can be symmetrically extended to elements in the maximal tensor product (textsf{C}_Aotimes _{max } textsf{C}^{otimes _{max } k}_B) for every (kin textbf{N}). Equivalently, the minimal tensor product of two cones is the intersection of the nested sets of k-extendible tensors. It is a natural question when the minimal tensor product (textsf{C}_Aotimes _{min } textsf{C}_B) coincides with the set of k-extendible tensors for some finite k. We show that this is universally the case for every cone (textsf{C}_A) if and only if (textsf{C}_B) 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.

甲乙双方共享的可分离量子态可以对称地扩展为甲乙双方共享的量子态(B_1,ldots ,B_k),对于每一个(kin textbf{N})。不可分离的量子态,即纠缠的量子态,不具备这一特性。这种现象被称为 "纠缠的一元性"。我们证明,一元性不仅是量子理论的一个特征,而且是一般凸锥对 (textsf{C}A) 和 (textsf{C}_B) 的最小张量积的特征:最小张量乘 (textsf{C}_Aotimes _{min } textsf{C}_B) 中的元素正是可以对称地扩展到最大张量乘 (textsf{C}_Aotimes _{max } textsf{C}^{otimes _{max } k}_B) 中元素的张量,对于每一个 (kin textbf{N}) 而言。等价地,两个锥体的最小张量积就是可扩展张量的嵌套集的交集。当最小张量积 (textsf{C}_Aotimes _{min } textsf{C}_B) 与某个有限 k 的可扩展张量集合重合时,这是一个很自然的问题。我们证明,对于每个圆锥体 (textsf{C}_A) 而言,当且仅当(textsf{C}_B) 是一个多面体圆锥体,其底面由简约的乘积给出时,情况都是如此。我们的证明利用了简约乘积的一个新特征,即仿射等价性,我们认为这一点具有独立的意义。
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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 Q1 MATHEMATICS Pub Date : 2024-08-06 DOI: 10.1007/s00208-024-02937-2
Nicolle González, Eugene Gorsky, José Simental

The double Dyck path algebra (mathbb {A}_{q,t}) 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 (mathbb {B}_{q,t}) 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 (mathbb {B}_{q,t}). 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.

双戴克路径代数(mathbb {A}_{q,t} )及其多项式表示最初是作为卡尔松和梅利特著名的洗牌定理证明的关键人物出现的。随后,第二位作者以及卡尔松和梅利特利用抛物线旗希尔伯特方案的 K 理论给出了等价代数 (mathbb {B}_{q,t}) 的几何表述。在本文中,我们开始系统地研究双戴克路径代数 (mathbb {B}_{q,t}) 的表示理论。我们定义了这个代数的自然扩展,并研究了它的校准表示。我们证明多项式表示是校准表示,并把它归入由满足特定条件的正集构造的校准表示大家族。我们还定义了这些表示的张量乘积和对偶,从而证明(在合适的条件下)校准表示的范畴一般是单义的。作为应用,我们证明了多项式表示的张量幂可以从抛物线吉塞克模空间的等变 K 理论中构造出来。
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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 Q1 MATHEMATICS Pub Date : 2024-08-03 DOI: 10.1007/s00208-024-02954-1
Jiayu Li, Shujing Pan

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.

在本文中,我们将通过在黎曼流形中引入一种平均曲率型流来研究等周问题,这种流被赋予了一个非三维共形向量场。这种流保留了星形超曲面所包围的有界域的体积,并在一定条件下减小了超曲面的面积。我们将证明该流的长期存在性和收敛性。因此,建立了此类域的等周不等式。特别是,我们解决了禀赋有封闭、非三维共形向量场的黎曼流形中星形超曲面的等周问题,其中包括关、李和王研究的一大类翘曲积空间。
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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 Q1 MATHEMATICS Pub Date : 2024-08-03 DOI: 10.1007/s00208-024-02956-z
Jun Geng, Zhongwei Shen

We establish resolvent estimates in (L^q) spaces for the Stokes operator in a bounded (C^1) domain (Omega ) in (mathbb {R}^{d}). As a corollary, it follows that the Stokes operator generates a bounded analytic semigroup in (L^q(Omega ; mathbb {C}^d)) for any (1< q< infty ) and (dge 2). The case of an exterior (C^1) domain is also studied.

我们在 (mathbb {R}^{d}) 的有界 (C^1) 域 (Omega ) 中建立了斯托克斯算子在 (L^q) 空间中的解析估计。作为一个推论,斯托克斯算子会在(L^q(Omega ; mathbb {C}^d))中生成一个有界的解析半群,适用于任何(1< q< infty )和(dge 2).我们还研究了外部(C^1)域的情况。
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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 Q1 MATHEMATICS Pub Date : 2024-07-30 DOI: 10.1007/s00208-024-02950-5
Baiqing Zhu

For a prime number (p>2) and a finite extension (F/mathbb {Q}_p), we explain the construction of the difference divisors on the unitary Rapoport–Zink spaces of hyperspecial level over (mathcal {O}_{breve{F}}), and the GSpin Rapoport–Zink spaces of hyperspecial level over (breve{mathbb {Z}}_{p}) associated to a minuscule cocharacter (mu ) and a basic element b. 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.

对于素数 (p>;2)和有限扩展 (F/mathbb {Q}_p),我们解释了在(mathcal {O}_{breve{F}}) 上超特一级的单元 Rapoport-Zink 空间上的差分子的构造、和与(mu )微小共字符和基本元素 b 相关联的 (breve{mathbb {Z}}_{p})上超特一级的 GSpin Rapoport-Zink 空间。我们用纯粹的变形理论方法证明了差分子的正则性,找到了特殊循环和差分子的形式光滑位置。
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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 Q1 MATHEMATICS Pub Date : 2024-07-29 DOI: 10.1007/s00208-024-02949-y
Joe Kramer-Miller, James Upton

The purpose of this article is to study Newton polygons of certain abelian L-functions on curves. Let X be a smooth affine curve over a finite field (mathbb {F}_q) and let (rho :pi _1(X) rightarrow mathbb {C}_p^times ) be a finite character of order (p^n). By previous work of the first author, the Newton polygon ({{,mathrm{text {NP}},}}(rho )) lies above a ‘Hodge polygon’ ({{,mathrm{text {HP}},}}(rho )) defined using ramification invariants of (rho ). In this article we study the contact between these two polygons. We prove that ({{,mathrm{text {NP}},}}(rho )) and ({{,mathrm{text {HP}},}}(rho )) share a vertex if and only if a corresponding vertex is shared between the Newton and Hodge polygons of ‘local’ L-functions associated to each ramified point of (rho ). As a consequence, we determine a necessary and sufficient condition for the coincidence of ({{,mathrm{text {NP}},}}(rho )) and ({{,mathrm{text {HP}},}}(rho )).

本文的目的是研究曲线上某些无边 L 函数的牛顿多边形。让 X 是一条有限域上的光滑仿射曲线,让 (rho :pi _1(X) rightarrow mathbb {C}_p^times ) 是一个阶为 (p^n) 的有限特征。根据第一作者之前的研究,牛顿多边形({{,mathrm{text {NP}},}}(rho )) 位于使用 (rho ) 的斜切不变式定义的 "霍奇多边形"({{,mathrm{text {HP}},}}(rho )) 的上方。本文将研究这两个多边形之间的接触。我们证明当且仅当与(rho )的每个斜切点相关联的 "局部 "L函数的牛顿多边形和霍奇多边形共享一个顶点时,({{,mathrm{text {NP},}}(rho )) 和({{,mathrm{text {HP},}}(rho )) 共享一个顶点。)因此,我们确定了 ({{,mathrm{text {NP},}}(rho )) 和 ({{,mathrm{text {HP},}}(rho )) 重合的必要条件和充分条件。)
{"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 Q1 MATHEMATICS Pub Date : 2024-07-28 DOI: 10.1007/s00208-024-02934-5
Shin-ichi Matsumura, Xiaojun Wu

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, (mathbb {Q})-conic bundles, and orbifold vector bundles.

在本文中,我们证明了一个非投影紧凑凯勒三折流形的nef反正交束,在一个有限的étale封面之前,是以下几种流形之一:第一奇恩类消失的流形;K3曲面与投影线的乘积;或二维环上的投影空间束。这一结果将曹霍林的投影流形结构定理扩展到了三维紧凑凯勒流形。为了证明这一点,我们利用直像剪、(mathbb {Q})-conic bundles和orbifold vector bundles的实在性,研究了具有nef反规范束的紧凑凯勒三流形的最小模型纲领。
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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 Q1 MATHEMATICS Pub Date : 2024-07-23 DOI: 10.1007/s00208-024-02947-0
Antonella Nastasi, Cintia Pacchiano Camacho

We prove boundedness, Hölder continuity, Harnack inequality results for local quasiminima to elliptic double phase problems of p-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.

我们证明了在一般度量空间背景下,p-拉普拉斯类型椭圆双相问题的有界性、赫尔德连续性和哈纳克不等式结果。证明采用变分法,以 De Giorgi 方法、细致的相位分析和本征几何估计为基础。
{"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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Mathematische Annalen
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