Mathematische Zeitschrift最新文献_第5页

Spherical adjunctions of stable $$infty $$ -categories and the relative S-construction 稳定 $$infty $$ 类的球面邻接和相对 S 构建

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-07-11 DOI: 10.1007/s00209-024-03549-x

Tobias Dyckerhoff, Mikhail Kapranov, Vadim Schechtman, Yan Soibelman

{"title":"Spherical adjunctions of stable $$infty $$ -categories and the relative S-construction","authors":"Tobias Dyckerhoff, Mikhail Kapranov, Vadim Schechtman, Yan Soibelman","doi":"10.1007/s00209-024-03549-x","DOIUrl":"https://doi.org/10.1007/s00209-024-03549-x","url":null,"abstract":"We develop the theory of semi-orthogonal decompositions and spherical functors in the framework of stable ({infty })-categories. We study the relative Waldhausen S-construction (S_bullet (F)) of the spherical functor F and show that it has a natural paracyclic structure (“rotation symmetry”). This fulfills a part of the general program of perverse schobers which are conjectural categorical upgrades of perverse sheaves. If we view a spherical functor as defining a schober on a disk, then each component (S_n(F)) of the S-construction gives a categorification of the cohomology of a perverse sheaf on a disk with support in a union of ((n+1)) closed arcs in the boundary. In other words, (S_n(F)) can be interpreted as the Fukaya category of the disk with coefficients in the schober and with support (“stops”) at the boundary arcs. The importance of the paracyclic structure is that it allows us to naturally associate the above data to disks on oriented surfaces. The action of the paracyclic rotation is a categorical analog of the monodromy of a perverse sheaf.","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"13 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141613707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 rotation number for the Schrödinger operator with $$alpha $$ -norm almost periodic measures 具有 $$alpha $$ -norm 几乎周期量的薛定谔算子的旋转数

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-07-09 DOI: 10.1007/s00209-024-03558-w

David Damanik, Gang Meng, Meirong Zhang, Zhe Zhou

引用次数: 0

Bounds for moments of Dirichlet L-functions to a fixed modulus 对固定模数的迪里夏特 L 函数矩的约束

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-07-08 DOI: 10.1007/s00209-024-03541-5

Peng Gao

引用次数: 0

Combinatorics of semi-toric degenerations of Schubert varieties in type C C 型舒伯特变种半oric退化的组合学

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-07-03 DOI: 10.1007/s00209-024-03531-7

Naoki Fujita, Yuta Nishiyama

引用次数: 0

Categorification of the plurigenera of Gorenstein normal surface singularities 戈伦斯坦法向曲面奇点的复元分类

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-07-02 DOI: 10.1007/s00209-024-03530-8

András Némethi, Gergő Schefler

引用次数: 0

Arithmetic progressions of squares and multiple Dirichlet series 算术级数的平方和多重德里赫特数列

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-07-01 DOI: 10.1007/s00209-024-03516-6

Thomas A. Hulse, Chan Ieong Kuan, David Lowry-Duda, Alexander Walker

引用次数: 0

Tilting and untilting for ideals in perfectoid rings 完美环中理想的倾斜和直到

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-06-28 DOI: 10.1007/s00209-024-03537-1

Dimitri Dine, Ryo Ishizuka

{"title":"Tilting and untilting for ideals in perfectoid rings","authors":"Dimitri Dine, Ryo Ishizuka","doi":"10.1007/s00209-024-03537-1","DOIUrl":"https://doi.org/10.1007/s00209-024-03537-1","url":null,"abstract":"For a perfectoid ring R of characteristic 0 with tilt (R^{flat }), we introduce and study a tilting map ((-)^{flat }) from the set of p-adically closed ideals of R to the set of ideals of (R^{flat }) and an untilting map ((-)^{sharp }) from the set of radical ideals of (R^{flat }) to the set of ideals of R. The untilting map ((-)^{sharp }) is defined purely algebraically and generalizes the analytically defined untilting map on closed radical ideals of a perfectoid Tate ring of characteristic p introduced in the first author’s previous work. We prove that the two maps $$begin{aligned} Jmapsto J^{flat }~text {and}~Imapsto I^{sharp } end{aligned}$$define an inclusion-preserving bijection between the set of ideals J of R such that the quotient R/J is perfectoid and the set of (p^{flat })-adically closed radical ideals of (R^{flat }), where (p^{flat }in R^{flat }) corresponds to a compatible system of p-power roots of a unit multiple of p in R. Finally, we prove that the maps ((-)^{flat }) and ((-)^{sharp }) send (closed) prime ideals to prime ideals and thus define a homeomorphism between the subspace of ({{,textrm{Spec},}}(R)) consisting of prime ideals (mathfrak {p}) of R such that (R/mathfrak {p}) is perfectoid and the subspace of ({{,textrm{Spec},}}(R^{flat })) consisting of (p^{flat })-adically closed prime ideals of (R^{flat }). In particular, we obtain a generalization and a new proof of the main result of the first author’s previous work which concerned prime ideals in perfectoid Tate rings.","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"155 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141531715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

When are KE-closed subcategories torsion-free classes? 什么情况下KE封闭子类是无扭类？

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-06-27 DOI: 10.1007/s00209-024-03536-2

Toshinori Kobayashi, Shunya Saito

引用次数: 0

Pseudolocality and completeness for nonnegative Ricci curvature limits of 3D singular Ricci flows 三维奇异利玛窦流的非负利玛窦曲率极限的伪位置性和完备性

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-06-27 DOI: 10.1007/s00209-024-03524-6

Albert Chau, Adam Martens

{"title":"Pseudolocality and completeness for nonnegative Ricci curvature limits of 3D singular Ricci flows","authors":"Albert Chau, Adam Martens","doi":"10.1007/s00209-024-03524-6","DOIUrl":"https://doi.org/10.1007/s00209-024-03524-6","url":null,"abstract":"Lai (Geom Topol 25:3629–3690, 2021) used singular Ricci flows, introduced by Kleiner and Lott (Acta Math 219(1):65–134, 2017), to construct a nonnegative Ricci curvature Ricci flow g(t) emerging from an arbitrary 3D complete noncompact Riemannian manifold ((M^3, g_0)) with nonnegative Ricci curvature. We show g(t) is complete for positive times provided (g_0) satisfies a volume ratio lower bound that approaches zero at spatial infinity. Our proof combines a pseudolocality result of Lai (2021) for singular flows, together with a pseudolocality result of Hochard (Short-time existence of the Ricci flow on complete, non-collapsed 3-manifolds with Ricci curvature bounded from below, 2016. arXiv:1603.08726) and Simon and Topping (J Differ Geom 122(3):467–518, 2022) for nonsingular flows. We also show that the construction of complete nonnegative complex sectional curvature flows by Cabezas-Rivas and Wilking (J Eur Math Soc (JEMS) 17(12):3153–3194, 2015) can be adapted here to show g(t) is complete for positive times provided (g_0) is a compactly supported perturbation of a nonnegative sectional curvature metric.","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"37 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 N-stable category N 稳定类别

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-06-27 DOI: 10.1007/s00209-024-03518-4

Jeremy R. B. Brightbill, Vanessa Miemietz

引用次数: 0