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Arithmetic fundamental lemma for the spherical Hecke algebra 球面赫克代数的算术基本定理
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-06-20 DOI: 10.1007/s00229-024-01572-0
Chao Li, Michael Rapoport, Wei Zhang
{"title":"Arithmetic fundamental lemma for the spherical Hecke algebra","authors":"Chao Li, Michael Rapoport, Wei Zhang","doi":"10.1007/s00229-024-01572-0","DOIUrl":"https://doi.org/10.1007/s00229-024-01572-0","url":null,"abstract":"<p>We define Hecke correspondences and Hecke operators on unitary RZ spaces and study their basic geometric properties, including a commutativity conjecture on Hecke operators. Then we formulate the arithmetic fundamental lemma conjecture for the spherical Hecke algebra. We also formulate a conjecture on the abundance of spherical Hecke functions with identically vanishing first derivative of orbital integrals. We prove these conjectures for the case <span>(textrm{U} (1)times textrm{U} (2))</span>.\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"13 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141510171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 relatively perfect Greenberg transform and cycle class maps 相对完美的格林伯格变换和循环类图
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-06-17 DOI: 10.1007/s00229-024-01576-w
Alessandra Bertapelle, Takashi Suzuki
{"title":"The relatively perfect Greenberg transform and cycle class maps","authors":"Alessandra Bertapelle, Takashi Suzuki","doi":"10.1007/s00229-024-01576-w","DOIUrl":"https://doi.org/10.1007/s00229-024-01576-w","url":null,"abstract":"<p>Given a scheme over a complete discrete valuation ring of mixed characteristic with perfect residue field, the Greenberg transform produces a new scheme over the residue field thicker than the special fiber. In this paper, we will generalize this transform to the case of imperfect residue field. We will then construct a certain kind of cycle class map defined on this generalized Greenberg transform applied to the Néron model of a semi-abelian variety, which takes values in the relatively perfect nearby cycle functor defined by Kato and the second author.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"16 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141525784","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Pureté de l’approximation forte sur le corps des fonctions d’une courbe algébrique complexe 复代数曲线函数场强近似的纯度
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-06-17 DOI: 10.1007/s00229-024-01560-4
Elyes Boughattas
{"title":"Pureté de l’approximation forte sur le corps des fonctions d’une courbe algébrique complexe","authors":"Elyes Boughattas","doi":"10.1007/s00229-024-01560-4","DOIUrl":"https://doi.org/10.1007/s00229-024-01560-4","url":null,"abstract":"<p>Over the function field of a complex algebraic curve, strong approximation off a non-empty finite set of places holds for the complement of a codimension 2 closed subset in a homogeneous space under a semisimple algebraic group, and for the complement of a codimension 2 closed subset in an affine smooth complete intersection of low degree.\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"19 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141530093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Root stacks and periodic decompositions 根堆栈和周期分解
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-06-15 DOI: 10.1007/s00229-024-01574-y
A. Bodzenta, W. Donovan
{"title":"Root stacks and periodic decompositions","authors":"A. Bodzenta, W. Donovan","doi":"10.1007/s00229-024-01574-y","DOIUrl":"https://doi.org/10.1007/s00229-024-01574-y","url":null,"abstract":"<p>For an effective Cartier divisor <i>D</i> on a scheme <i>X</i> we may form an <span>({n}^{text {th}})</span> root stack. Its derived category is known to have a semiorthogonal decomposition with components given by <i>D</i> and <i>X</i>. We show that this decomposition is <span>(2n)</span>-periodic. For <span>(n=2)</span> this gives a purely triangulated proof of the existence of a known spherical functor, namely the pushforward along the embedding of <i>D</i>. For <span>(n &gt; 2)</span> we find a higher spherical functor in the sense of recent work of Dyckerhoff et al. (<i>N</i>-spherical functors and categorification of Euler’s continuants. arXiv:2306.13350, 2023). We use a realization of the root stack construction as a variation of GIT, which may be of independent interest.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"46 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141525785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
On p-adic Siegel–Eisenstein series from a point of view of the theory of mod $$p^m$$ singular forms 从模$p^m$$奇异形式理论的角度论 p-阿代尔西格尔-爱森斯坦数列
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-06-13 DOI: 10.1007/s00229-024-01571-1
Siegfried Böcherer, Toshiyuki Kikuta
{"title":"On p-adic Siegel–Eisenstein series from a point of view of the theory of mod $$p^m$$ singular forms","authors":"Siegfried Böcherer, Toshiyuki Kikuta","doi":"10.1007/s00229-024-01571-1","DOIUrl":"https://doi.org/10.1007/s00229-024-01571-1","url":null,"abstract":"<p>We show that the <i>p</i>-adic Siegel–Eisenstein series of general degree attached to two kind of number sequences are both linear combinations of genus theta series of level dividing <i>p</i>, by applying the theory of mod <i>p</i>-power singular forms. As special cases of this result, we derive the results of Nagaoka and Katsurada–Nagaoka.\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"38 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141525786","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
An inclusion–exclusion principle for tautological sheaves on Hilbert schemes of points 点的希尔伯特方案上的同调卷的包含-排除原理
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-06-11 DOI: 10.1007/s00229-024-01570-2
Xiaowen Hu
{"title":"An inclusion–exclusion principle for tautological sheaves on Hilbert schemes of points","authors":"Xiaowen Hu","doi":"10.1007/s00229-024-01570-2","DOIUrl":"https://doi.org/10.1007/s00229-024-01570-2","url":null,"abstract":"<p>We show an equation of Euler characteristics of tautological sheaves on Hilbert schemes of points on the fibers of a double point degeneration. This equation resembles a computation of such Euler characteristics via a combinatorial inclusion–exclusion principle. As a consequence, we show the existence of universal polynomials for the Euler characteristics of tautological sheaves on the Hilbert scheme of points on smooth proper algebraic spaces. We apply this result to a conjecture of Zhou on tautological sheaves on Hilbert schemes of points, and reduce the conjecture to the cases of products of projective spaces. Our main tools are good degenerations and algebraic cobordism.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"4 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141510172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Full exceptional collections of line bundles on the blow-up of $${mathbb {P}}^{5}$$ along Segre threefold $${mathbb {P}}^{5}$ 沿塞格雷三折吹大的线束的全例外集合
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-06-04 DOI: 10.1007/s00229-024-01569-9
Tomoki Yoshida
{"title":"Full exceptional collections of line bundles on the blow-up of $${mathbb {P}}^{5}$$ along Segre threefold","authors":"Tomoki Yoshida","doi":"10.1007/s00229-024-01569-9","DOIUrl":"https://doi.org/10.1007/s00229-024-01569-9","url":null,"abstract":"<p>We prove Kuznetsov’s conjecture on the fullness of exceptional collections in the line bundles case for the blow-up of <span>({mathbb {P}}^{5})</span> along the image of Segre threefold <span>({mathbb {P}}^{1}times {mathbb {P}}^{2})</span> and its hyperplane section.\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141255172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 strata in Levi subgroups 列维分组中的牛顿层
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-06-04 DOI: 10.1007/s00229-024-01566-y
Felix Schremmer
{"title":"Newton strata in Levi subgroups","authors":"Felix Schremmer","doi":"10.1007/s00229-024-01566-y","DOIUrl":"https://doi.org/10.1007/s00229-024-01566-y","url":null,"abstract":"<p>Certain Iwahori double cosets in the loop group of a reductive group, known under the names of <i>P</i>-alcoves or <span>((J,w,delta ))</span>-alcoves, play an important role in the study of affine Deligne–Lusztig varieties. For such an Iwahori double coset, its Newton stratification is related to the Newton stratification of an Iwahori double coset in a Levi subgroup. We study this relationship further, providing in particular a bijection between the occurring Newton strata. As an application, we prove a conjecture of Dong-Gyu Lim, giving a non-emptiness criterion for basic affine Deligne–Lusztig varieties.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"6 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141255173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A note about the generic irreducibility of the spectrum of the Laplacian on homogeneous spaces 关于同质空间上拉普拉斯频谱一般不可还原性的说明
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-06-03 DOI: 10.1007/s00229-024-01567-x
Diego S. de Oliveira, Marcus A. M. Marrocos
{"title":"A note about the generic irreducibility of the spectrum of the Laplacian on homogeneous spaces","authors":"Diego S. de Oliveira, Marcus A. M. Marrocos","doi":"10.1007/s00229-024-01567-x","DOIUrl":"https://doi.org/10.1007/s00229-024-01567-x","url":null,"abstract":"<p>Petrecca and Röser (Mathematische Zeitschrift 291:395–419, 2018) and Schueth (Ann Global Anal Geom 52:187–200, 2017) had shown that for a generic <i>G</i>-invariant metric <i>g</i> on certain compact homogeneous spaces <span>(M=G/K)</span> (including symmetric spaces of rank 1 and some Lie groups), the spectrum of the Laplace-Beltrami operator <span>(Delta _g)</span> was real <i>G</i>-simple. The same is not true for the complex version of <span>(Delta _g)</span> when there is a presence of representations of complex or quaternionic type. We show that these types of representations induces a <span>(Q_8)</span>-action that commutes with the Laplacian in such way that <i>G</i>-properties of the real version of the operator have to be understood as <span>((Q_8 times G))</span>-properties on its corresponding complex version.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"101 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141255580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
W-triviality of low dimensional manifolds 低维流形的 W 三维性
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-06-03 DOI: 10.1007/s00229-024-01575-x
Aritra C. Bhattacharya, Bikramjit Kundu, Aniruddha C. Naolekar
{"title":"W-triviality of low dimensional manifolds","authors":"Aritra C. Bhattacharya, Bikramjit Kundu, Aniruddha C. Naolekar","doi":"10.1007/s00229-024-01575-x","DOIUrl":"https://doi.org/10.1007/s00229-024-01575-x","url":null,"abstract":"<p>A space <i>X</i> is <i>W</i>-trivial if for every real vector bundle <span>(alpha )</span> over <i>X</i> the total Stiefel-Whitney class <span>(w(alpha ))</span> is 1. It follows from a result of Milnor that if <i>X</i> is an orientable closed smooth manifold of dimension 1, 2, 4 or 8, then <i>X</i> is not <i>W</i>-trivial. In this note we completely characterize <i>W</i>-trivial orientable connected closed smooth manifolds in dimensions 3, 5 and 6. In dimension 7, we describe necessary conditions for an orientable connected closed smooth 7-manifold to be <i>W</i>-trivial.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"66 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141255171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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