Asterisque最新文献

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La théorie de Hodge des bimodules de Soergel (d'après Soergel et Elias-Williamson) Soergel的Hodge双模理论(基于Soergel和Elias-Williamson)
IF 1.1 4区 数学
Asterisque Pub Date : 2017-11-07 DOI: 10.24033/ast.1083
S. Riche
{"title":"La théorie de Hodge des bimodules de Soergel (d'après Soergel et Elias-Williamson)","authors":"S. Riche","doi":"10.24033/ast.1083","DOIUrl":"https://doi.org/10.24033/ast.1083","url":null,"abstract":"Soergel bimodules are certain bimodules over polynomial algebras, associated with Coxeter groups, and introduced by Soergel in the 1990's while studying the category O of complex semisimple Lie algebras. Even though their definition is algebraic and rather elementary, some of their crucial properties were known until recently only in the case of crystallographic Coxeter groups, where these bimodules can be interpreted in terms of equivariant cohomology of Schubert varieties. In recent work Elias and Williamson have proved these properties in full generality by showing that these bimodules possess \"Hodge type\" properties. These results imply positivity of Kazhdan-Lusztig polynomials in full generality, and provide an algebraic proof of the Kazhdan-Lusztig conjecture.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2017-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48296675","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: 5
Arithmetic of Borcherds products Borcherds乘积的算术
IF 1.1 4区 数学
Asterisque Pub Date : 2017-10-01 DOI: 10.24033/ast.1128
Benjamin J. Howard, Keerthi Madapusi Pera
{"title":"Arithmetic of Borcherds products","authors":"Benjamin J. Howard, Keerthi Madapusi Pera","doi":"10.24033/ast.1128","DOIUrl":"https://doi.org/10.24033/ast.1128","url":null,"abstract":"We compute the divisors of Borcherds products on integral models of orthogonal Shimura varieties. As an application, we obtain an integral version of a theorem of Borcherds on the modularity of a generating series of special divisors.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2017-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48201260","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: 17
Projective cocycles over SL(2,R) actions: measures invariant under the upper triangular group SL(2,R)作用上的射影环:上三角群下的测度不变
IF 1.1 4区 数学
Asterisque Pub Date : 2017-09-08 DOI: 10.24033/ast.1103
C. Bonatti, A. Eskin, A. Wilkinson
{"title":"Projective cocycles over SL(2,R) actions: measures invariant under the upper triangular group","authors":"C. Bonatti, A. Eskin, A. Wilkinson","doi":"10.24033/ast.1103","DOIUrl":"https://doi.org/10.24033/ast.1103","url":null,"abstract":"We consider the action of $SL(2,mathbb{R})$ on a vector bundle $mathbf{H}$ preserving an ergodic probability measure $nu$ on the base $X$. Under an irreducibility assumption on this action, we prove that if $hatnu$ is any lift of $nu$ to a probability measure on the projectivized bunde $mathbb{P}(mathbf{H})$ that is invariant under the upper triangular subgroup, then $hat nu$ is supported in the projectivization $mathbb{P}(mathbf{E}_1)$ of the top Lyapunov subspace of the positive diagonal semigroup. We derive two applications. First, the Lyapunov exponents for the Kontsevich-Zorich cocycle depend continuously on affine measures, answering a question in [MMY]. Second, if $mathbb{P}(mathbf{V})$ is an irreducible, flat projective bundle over a compact hyperbolic surface $Sigma$, with hyperbolic foliation $mathcal{F}$ tangent to the flat connection, then the foliated horocycle flow on $T^1mathcal{F}$ is uniquely ergodic if the top Lyapunov exponent of the foliated geodesic flow is simple. This generalizes results in [BG] to arbitrary dimension.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2017-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47512850","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: 11
A closing lemma for polynomial automorphisms of C² C²多项式自同构的一个闭引理
IF 1.1 4区 数学
Asterisque Pub Date : 2017-09-05 DOI: 10.24033/ast.1098
Romain Dujardin
{"title":"A closing lemma for polynomial automorphisms of C²","authors":"Romain Dujardin","doi":"10.24033/ast.1098","DOIUrl":"https://doi.org/10.24033/ast.1098","url":null,"abstract":"We prove that for a polynomial diffeomorphism of C^2 , the support of any invariant measure, apart from a few obvious cases, is contained in the closure of the set of saddle periodic points.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2017-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43961915","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: 6
Equivariant $mathcal D$-modules on rigid analytic spaces 刚性分析空间上的等变$mathcal D$-模
IF 1.1 4区 数学
Asterisque Pub Date : 2017-08-24 DOI: 10.24033/AST.1145
K. Ardakov
{"title":"Equivariant $mathcal D$-modules on rigid analytic spaces","authors":"K. Ardakov","doi":"10.24033/AST.1145","DOIUrl":"https://doi.org/10.24033/AST.1145","url":null,"abstract":"We define coadmissible equivariant $mathcal{D}$-modules on smooth rigid analytic spaces and relate them to admissible locally analytic representations of semisimple $p$-adic Lie groups.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2017-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43717567","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: 6
Linear systems of wave equations on cosmological backgrounds with convergent asymptotics 具有收敛渐近性的宇宙学背景上的波动方程线性系统
IF 1.1 4区 数学
Asterisque Pub Date : 2017-07-10 DOI: 10.24033/ast.1123
Hans Ringstrom
{"title":"Linear systems of wave equations on cosmological backgrounds with convergent asymptotics","authors":"Hans Ringstrom","doi":"10.24033/ast.1123","DOIUrl":"https://doi.org/10.24033/ast.1123","url":null,"abstract":"The subject of the article is linear systems of wave equations on cosmological backgrounds with convergent asymptotics. The condition of convergence corresponds to the requirement that the second fundamental form, when suitably normalised, converges. The model examples are the Kasner solutions. The main result of the article is optimal energy estimates. However, we also derive asymptotics and demonstrate that the leading order asymptotics can be specified. It is sometimes argued that if the factors multiplying the spatial derivatives decay exponentially (for a system of wave equations), then the spatial derivatives can be ignored. This line of reasoning is incorrect: we give examples of equations such that 1) the factors multiplying the spatial derivatives decay exponentially, 2) the factors multiplying the time derivatives are constants, 3) the energies of individual modes of solutions asymptotically decay exponentially, and 4) the energies of generic solutions grow as $e^{e^{t}}$ as $trightarrow infty$. When the factors multiplying the spatial derivatives grow exponentially, the Fourier modes of solutions oscillate with a frequency that grows exponentially. To obtain asymptotics, we fix a mode and consider the net evolution over one period. Moreover, we replace the evolution (over one period) with a matrix multiplication. We cannot calculate the matrices, but we approximate them. To obtain the asymptotics we need to calculate a matrix product where there is no bound on the number of factors, and where each factor can only be approximated. Nevertheless, we obtain detailed asymptotics. In fact, it is possible to isolate an overall behaviour (growth/decay) from the (increasingly violent) oscillatory behaviour. Moreover, we are also in a position to specify the leading order asymptotics.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2017-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43207179","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: 24
The Vinogradov Mean Value Theorem (after Wooley, and Bourgain, Demeter and Guth) 维诺格拉多夫中值定理(源自Woolley、Bourgain、Demeter和Guth)
IF 1.1 4区 数学
Asterisque Pub Date : 2017-07-01 DOI: 10.24033/ast.1072
L. Pierce
{"title":"The Vinogradov Mean Value Theorem (after Wooley, and Bourgain, Demeter and Guth)","authors":"L. Pierce","doi":"10.24033/ast.1072","DOIUrl":"https://doi.org/10.24033/ast.1072","url":null,"abstract":"This is the expository essay that accompanies my Bourbaki Seminar on 17 June 2017 on the landmark proof of the Vinogradov Mean Value Theorem, and the two approaches developed in the work of Wooley and of Bourgain, Demeter and Guth.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41836864","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: 33
Geometric hypoelliptic Laplacian and orbital integrals (after Bismut, Lebeau, and Shen) 几何准椭圆拉普拉斯积分和轨道积分(继Bismut、Lebeau和Shen之后)
IF 1.1 4区 数学
Asterisque Pub Date : 2017-04-26 DOI: 10.24033/ast.1068
X. Ma
{"title":"Geometric hypoelliptic Laplacian and orbital integrals (after Bismut, Lebeau, and Shen)","authors":"X. Ma","doi":"10.24033/ast.1068","DOIUrl":"https://doi.org/10.24033/ast.1068","url":null,"abstract":"About 15 years ago, Bismut gave a natural construction of a Hodge theory for a hypoelliptic Laplacian acting on the total space of the cotangent bundle of a Riemannian manifold. This operator interpolates between the classical elliptic Laplacian on the base and the generator of the geodesic flow. We will describe recent developments of the theory of hypoelliptic Laplacians, in particular the explicit formula obtained by Bismut for orbital integrals and the recent solution by Shen of Fried's conjecture (dating back to 1986) for locally symmetric spaces. The conjecture predicts the equality of the analytic torsion and the value at 0 of the dynamic zeta function.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2017-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47421577","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: 7
Avancées concernant les R-matrices et leurs applications (d’après Maulik-Okounkov, Kang-Kashiwara-Kim-Oh, ...) r矩阵及其应用的进展(根据Maulik-Okounkov, Kang-Kashiwara-Kim-Oh,…)
IF 1.1 4区 数学
Asterisque Pub Date : 2017-04-20 DOI: 10.24033/ast.1067
David Hernandez
{"title":"Avancées concernant les R-matrices et leurs applications (d’après Maulik-Okounkov, Kang-Kashiwara-Kim-Oh, ...)","authors":"David Hernandez","doi":"10.24033/ast.1067","DOIUrl":"https://doi.org/10.24033/ast.1067","url":null,"abstract":"R-matrices are the solutions of the Yang-Baxter equation. At the origin of the quantum group theory, they may be interpreted as intertwining operators. Recent advances have been made independently in different directions. Maulik-Okounkov have given a geometric approach to R-matrices with new tools in symplectic geometry, the stable envelopes. Kang-Kashiwara-Kim-Oh proved a conjecture on the categorification of cluster algebras by using R-matrices in a crucial way. Eventually, a better understanding of the action of transfer-matrices obtained from R-matrices led to the proof of several conjectures about the corresponding quantum integrable systems.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2017-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44064184","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: 19
Modularity of generating series of divisors on unitary Shimura varieties II: arithmetic applications 酉Shimura变上产生除数级数的模块化II:算术应用
IF 1.1 4区 数学
Asterisque Pub Date : 2017-02-25 DOI: 10.24033/ast.1127
J. Bruinier, Benjamin J. Howard, S. Kudla, M. Rapoport, Tonghai Yang
{"title":"Modularity of generating series of divisors on unitary Shimura varieties II: arithmetic applications","authors":"J. Bruinier, Benjamin J. Howard, S. Kudla, M. Rapoport, Tonghai Yang","doi":"10.24033/ast.1127","DOIUrl":"https://doi.org/10.24033/ast.1127","url":null,"abstract":"We form generating series of special divisors, valued in the Chow group and in the arithmetic Chow group, on the compactified integral model of a Shimura variety associated to a unitary group of signature (n-1,1), and prove their modularity. The main ingredient of the proof is the calculation of the vertical components appearing in the divisor of a Borcherds product on the integral model.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2017-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43536664","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: 28
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