Compositio Mathematica最新文献

英文中文

COM volume 160 issue 6 Cover and Back matter COM 第 160 卷第 6 期封面和封底

IF 1.8 1区数学 Q1 Mathematics

Compositio Mathematica

Pub Date : 2024-05-23 DOI: 10.1112/s0010437x23007844

引用次数: 0

A geometric p-adic Simpson correspondence in rank one 一阶几何 p-adic Simpson 对应关系

IF 1.8 1区数学 Q1 Mathematics

Compositio Mathematica

Pub Date : 2024-05-21 DOI: 10.1112/s0010437x24007024

Ben Heuer

For any smooth proper rigid space $X$ over a complete algebraically closed extension $K$ of $mathbb {Q}_p$ we give a geometrisation of the $p$-adic Simpson correspondence of rank one in terms of analytic moduli spaces: the $p$-adic character variety is canonically an étale twist of the moduli space of topologically torsion Higgs line bundles over the Hitchin base. This also eliminates the choice of an exponential. The key idea is to relate both sides to moduli spaces of $v$-line bundles. As an application, we study a major open question in $p$-adic non-abelian Hodge theory raised by Faltings, namely which Higgs bundles correspond to continuous representations under the $p$-adic Simpson correspondence. We answer this question in rank one by describing the

对于在$mathbb {Q}_p$ 的完整代数封闭扩展$K$上的任何光滑适当刚性空间$X$，我们给出了秩为一的$p$-adic Simpson对应的解析模空间的几何解析：$p$-adic character variety典型地是希钦基上拓扑扭转希格斯线束的模空间的褶曲。这也消除了指数的选择。关键的思路是把两边都与 $v$ 线束的模空间联系起来。作为应用，我们研究了法尔廷斯提出的p$-adic非阿贝尔霍奇理论中的一个主要未决问题，即哪些希格斯束对应于p$-adic辛普森对应下的连续表示。我们通过描述连续字符 $pi ^{mathrm {acute {e}t}}_1(X)to K^times$ 在模空间方面的本质映像来回答这个问题：对于在 $K=mathbb {C}_p$ 上的投影 $X$，它是由希格斯线束给出的，就像复几何学中的奇恩类消失一样。然而，一般来说，正确的条件是更严格的假设，即底层线束是拓扑群 $operatorname {Pic}(X)$ 中的拓扑扭转元素。

引用次数: 0

Thin links and Conway spheres 薄链接和康威球

IF 1.8 1区数学 Q1 Mathematics

Compositio Mathematica

Pub Date : 2024-05-20 DOI: 10.1112/s0010437x24007152

Artem Kotelskiy, Liam Watson, Claudius Zibrowius

When restricted to alternating links, both Heegaard Floer and Khovanov homology concentrate along a single diagonal $delta$-grading. This leads to the broader class of thin links that one would like to characterize without reference to the invariant in question. We provide a relative version of thinness for tangles and use this to characterize thinness via tangle decompositions along Conway spheres. These results bear a strong resemblance to the L-space gluing theorem for three-manifolds with torus boundary. Our results are based on certain immersed curve invariants for Conway tangles, namely the Heegaard Floer invariant $operatorname {HFT}$ and the Khovanov invariant $widetilde {operatorname {Kh}}$ that were developed by the authors in previous works.

当局限于交替链接时，Heegaard Floer 和 Khovanov 同调都集中在单一对角线 $delta$ 等级上。这就引出了我们想要描述的更广泛的薄链接类别，而无需参考相关的不变量。我们为缠结提供了薄度的相对版本，并利用它通过沿着康威球的缠结分解来表征薄度。这些结果与具有环边界的三芒星的 L 空间胶合定理非常相似。我们的结果基于康威纠结的某些沉浸曲线不变式，即作者在之前的著作中提出的希嘉德-弗洛尔不变式 $operatorname {HFT}$ 和霍瓦诺夫不变式 $widetilde {operatorname {Kh}}$。

{"title":"Thin links and Conway spheres","authors":"Artem Kotelskiy, Liam Watson, Claudius Zibrowius","doi":"10.1112/s0010437x24007152","DOIUrl":"https://doi.org/10.1112/s0010437x24007152","url":null,"abstract":"When restricted to alternating links, both Heegaard Floer and Khovanov homology concentrate along a single diagonal <img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240517100304785-0216:S0010437X24007152:S0010437X24007152_inline1.png\">$delta$</img>-grading. This leads to the broader class of thin links that one would like to characterize without reference to the invariant in question. We provide a relative version of thinness for tangles and use this to characterize thinness via tangle decompositions along Conway spheres. These results bear a strong resemblance to the L-space gluing theorem for three-manifolds with torus boundary. Our results are based on certain immersed curve invariants for Conway tangles, namely the Heegaard Floer invariant <img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240517100304785-0216:S0010437X24007152:S0010437X24007152_inline2.png\">$operatorname {HFT}$</img> and the Khovanov invariant <img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240517100304785-0216:S0010437X24007152:S0010437X24007152_inline3.png\">$widetilde {operatorname {Kh}}$</img> that were developed by the authors in previous works.","PeriodicalId":55232,"journal":{"name":"Compositio Mathematica","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153114","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}

引用次数: 0

Twisted Whittaker category on affine flags and the category of representations of the mixed quantum group 仿射旗上的扭曲惠特克范畴和混合量子群的表示范畴

IF 1.8 1区数学 Q1 Mathematics

Compositio Mathematica

Pub Date : 2024-05-13 DOI: 10.1112/s0010437x24007139

Ruotao Yang

Let $G$ be a reductive group, and let $check {G}$ be its Langlands dual group. Arkhipov and Bezrukavnikov proved that the Whittaker category on the affine flags ${operatorname {Fl}}_G$ is equivalent to the category of $check {G}$-equivariant quasi-coherent sheaves on the Springer resolution of the nilpotent cone. This paper proves this theorem in the quantum case. We show that the twisted Whittaker category on ${operatorname {Fl}}_G$ and the category of representations of the mixed quantum group are equivalent. In particular, we prove that the quantum category $mathsf {O}$ is equivalent to the twisted Whittaker category on ${operatorname {Fl}}_G$ in the generic case. The strong version of our main theorem claims a motivic equivalence between the Whittaker category on ${operatorname {Fl}}_

让 $G$ 是一个还原群，让 $check {G}$ 是它的朗兰兹对偶群。Arkhipov 和 Bezrukavnikov 证明了仿射旌旗 ${operatorname {Fl}}_G$ 上的惠特克范畴等价于零势锥的 Springer 分辨率上的 $check {G}$ 等价准相干剪切范畴。本文在量子情形中证明了这一定理。我们证明了 ${operatorname {Fl}}_G$ 上的扭曲惠特克范畴和混合量子群的表示范畴是等价的。特别是，我们证明了在一般情况下，量子范畴 $mathsf {O}$ 与 ${operatorname {Fl}}_G$ 上的扭曲维特克范畴是等价的。我们的主定理的强版本声称，${operatorname {Fl}}_G$ 上的维特克类别与因式分解模块类别之间存在动机等价性，这在德拉姆设定、贝蒂设定和$ell$-adic设定中都成立。

引用次数: 0

A solution to the Erdős–Sárközy–Sós problem on asymptotic Sidon bases of order 3 厄尔多斯-萨尔科齐-索斯问题在 3 阶西顿渐近基上的求解

IF 1.8 1区数学 Q1 Mathematics

Compositio Mathematica

Pub Date : 2024-05-10 DOI: 10.1112/s0010437x24007140

Cédric Pilatte

A set $Ssubset {mathbb {N}}$ is a Sidon set if all pairwise sums $s_1+s_2$ (for $s_1, s_2in S$, $s_1leqslant s_2$) are distinct. A set $Ssubset {mathbb {N}}$ is an asymptotic basis of order 3 if every sufficiently large integer $n$ can be written as the sum of three elements of $S$. In 1993, Erdős, Sárközy and Sós asked whether there exists a set $S$ with both properties. We answer this question in the affirmative. Our proof relies on a deep result of Sawin on the $mathbb {F}_q[t]$<

如果所有成对的和 $s_1+s_2$ （对于 S$中的 $s_1，s_2/$，$s_1/leqslant s_2$）都是不同的，那么一个集合 $Ssubset {mathbb {N}}$ 就是一个西顿集合。如果每个足够大的整数 $n$ 都可以写成 $S$ 的三个元素之和，那么集合 $S$ 的子集 {mathbb {N}}$ 就是阶数为 3 的渐近基。1993 年，厄尔多斯、萨尔科齐和索斯提出了是否存在同时具有这两种性质的集合 $S$。我们的回答是肯定的。我们的证明依赖于萨温关于$mathbb {F}_q[t]$ --蒙哥马利对冯-曼戈尔德函数卷积的猜想的一个深层结果。

引用次数: 0

Rational Hodge isometries of hyper-Kähler varieties of type are algebraic 超凯勒变类的有理霍奇等分线是代数的

IF 1.8 1区数学 Q1 Mathematics

Compositio Mathematica

Pub Date : 2024-05-07 DOI: 10.1112/s0010437x24007048

Eyal Markman

Let $X$ and $Y$ be compact hyper-Kähler manifolds deformation equivalent to the Hilbert scheme of length $n$ subschemes of a $K3$ surface. A class in $H^{p,p}(Xtimes Y,{mathbb {Q}})$ is an analytic correspondence, if it belongs to the subring generated by Chern classes of coherent analytic sheaves. Let $f:H^2(X,{mathbb {Q}})rightarrow H^2(Y,{mathbb {Q}})$ be a rational Hodge isometry with respect to the Beauville–Bogomolov–Fujiki pairings. We prove that $f$ is induced by an analytic correspondence. We furthermore lift $f$ to an analytic correspondence

假设 $X$ 和 $Y$ 是紧凑超凯勒流形，其变形等价于 $K3$ 曲面的长度为 $n$ 的希尔伯特子方案。如果$H^{p,p}(X/times Y,{mathbb {Q}})$中的一个类属于相干解析剪切的切恩类所产生的子环，那么这个类就是解析对应。让 $f:H^2(X,{mathbb {Q}})rightarrow H^2(Y,{mathbb {Q}})$ 是关于博维尔-博戈莫洛夫-富士基配对的有理霍奇等距。我们证明 $f$ 是由解析对应关系诱导的。我们进一步把 $f$ 提升到一个解析对应 $tilde {f}：H^*(X,{mathbb{Q}})[2n]rightarrow H^*(Y,{mathbb{Q}})[2n]$，这是一个关于向井配对的霍奇等距法，它保留了直到符号的等级。当 $X$ 和 $Y$ 是投影的时候，对应的 $f$ 和 $tilde {f}$ 是代数的。

引用次数: 0

Weak approximation on the norm one torus 一规范环上的弱近似值

IF 1.8 1区数学 Q1 Mathematics

Compositio Mathematica

Pub Date : 2024-05-06 DOI: 10.1112/s0010437x24007103

P. Koymans, N. Rome

For any abelian group $A$, we prove an asymptotic formula for the number of $A$-extensions $K/mathbb {Q}$ of bounded discriminant such that the associated norm one torus $R_{K/mathbb {Q}}^1 mathbb {G}_m$ satisfies weak approximation. We are also able to produce new results on the Hasse norm principle and to provide new explicit values for the leading constant in some instances of Malle's conjecture.

对于任意无性群 $A$，我们证明了一个关于有界判别式的 $A$ 扩展 $K/mathbb {Q}$ 的渐近公式，该扩展使得相关的一规范环 $R_{K/mathbb {Q}}^1 mathbb {G}_m$ 满足弱逼近。我们还能得出关于哈塞规范原理的新结果，并为马勒猜想的某些实例中的前导常数提供新的明确值。

引用次数: 0

Spectral decomposition of genuine cusp forms over global function fields 全局函数域上真正顶点形式的谱分解

IF 1.8 1区数学 Q1 Mathematics

Compositio Mathematica

Pub Date : 2024-05-06 DOI: 10.1112/s0010437x24007127

Yifei Zhao

We prove the geometric Satake equivalence for étale metaplectic covers of reductive group schemes and extend the Langlands parametrization of V. Lafforgue to genuine cusp forms defined on their associated covering groups.

我们证明了还原群方案的 étale metaplectic 覆盖的几何 Satake 等价性，并将 V. Lafforgue 的 Langlands 参数化扩展到定义在其相关覆盖群上的真正尖顶形式。

引用次数: 0

On Donkin's tilting module conjecture II: counterexamples 关于唐金的倾斜模猜想 II：反例

IF 1.8 1区数学 Q1 Mathematics

Compositio Mathematica

Pub Date : 2024-05-02 DOI: 10.1112/s0010437x24007115

Christopher P. Bendel, Daniel K. Nakano, Cornelius Pillen, Paul Sobaje

In this paper we produce infinite families of counterexamples to Jantzen's question posed in 1980 on the existence of Weyl $p$-filtrations for Weyl modules for an algebraic group and Donkin's tilting module conjecture formulated in 1990. New techniques to exhibit explicit examples are provided along with methods to produce counterexamples in large rank from counterexamples in small rank. Counterexamples can be produced via our methods for all groups other than when the root system is of type ${rm A}_{n}$ or ${rm B}_{2}$.

在本文中，我们针对杨岑在 1980 年提出的关于代数群的 Weyl 模块是否存在 Weyl $p$ 滤波的问题，以及唐金在 1990 年提出的倾斜模块猜想，提出了无穷系列的反例。本书提供了展示明确例子的新技术，以及从小秩反例产生大秩反例的方法。除了根系统是 ${rm A}_{n}$ 或 ${rm B}_{2}$ 类型之外，所有群都可以通过我们的方法产生反例。

引用次数: 0

COM volume 160 issue 5 Cover and Front matter COM 第 160 卷第 5 期封面和封底

IF 1.8 1区数学 Q1 Mathematics

Compositio Mathematica

Pub Date : 2024-05-01 DOI: 10.1112/s0010437x23007819

引用次数: 0

首页上一页

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Compositio Mathematica

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀

微信

客服QQ

扫码关注我们

反馈

Book学术文献互助群
群号：481959085

文献互助智能选刊最新文献互助须知联系我们：info@booksci.cn

Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。