Journal of the Institute of Mathematics of Jussieu最新文献

EXCEPTIONAL SIMPLE REAL LIE ALGEBRAS AND VIA CONTACTIFICATIONS 非凡简单实线性代数和通过接触化

IF 0.9 2区数学

Journal of the Institute of Mathematics of Jussieu Pub Date : 2024-07-03 DOI: 10.1017/s1474748024000173

Paweł Nurowski

{"title":"EXCEPTIONAL SIMPLE REAL LIE ALGEBRAS AND VIA CONTACTIFICATIONS","authors":"Paweł Nurowski","doi":"10.1017/s1474748024000173","DOIUrl":"https://doi.org/10.1017/s1474748024000173","url":null,"abstract":"In Cartan’s PhD thesis, there is a formula defining a certain rank 8 vector distribution in dimension 15, whose algebra of authomorphism is the split real form of the simple exceptional complex Lie algebra $mathfrak {f}_4$ . Cartan’s formula is written in the standard Cartesian coordinates in $mathbb {R}^{15}$ . In the present paper, we explain how to find analogous formulae for the flat models of any bracket generating distribution $mathcal D$ whose symbol algebra $mathfrak {n}({mathcal D})$ is constant and 2-step graded, $mathfrak {n}({mathcal D})=mathfrak {n}_{-2}oplus mathfrak {n}_{-1}$ . The formula is given in terms of a solution to a certain system of linear algebraic equations determined by two representations $(rho ,mathfrak {n}_{-1})$ and $(tau ,mathfrak {n}_{-2})$ of a Lie algebra $mathfrak {n}_{00}$ contained in the ","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141527979","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

COHOMOLOGIE DE DE RHAM DU REVÊTEMENT MODÉRÉ DE L’ESPACE DE DRINFELD 德林菲尔德空间温和覆盖的德拉姆同调

IF 0.9 2区数学

Journal of the Institute of Mathematics of Jussieu Pub Date : 2024-05-28 DOI: 10.1017/s1474748024000082

Damien Junger

{"title":"COHOMOLOGIE DE DE RHAM DU REVÊTEMENT MODÉRÉ DE L’ESPACE DE DRINFELD","authors":"Damien Junger","doi":"10.1017/s1474748024000082","DOIUrl":"https://doi.org/10.1017/s1474748024000082","url":null,"abstract":"Résumé Dans cet article, nous étudions la cohomologie de de Rham du premier revêtement de la tour de Drinfel’d. En particulier, nous obtenons une preuve purement locale du fait que la partie supercuspidale réalise la correspondance de Jacquet-Langlands locale pour $mathrm {GL}_n$ en la comparant à la cohomologie rigide de certaines variétés de Deligne-Lusztig. Les représentations obtenues sont analogues à celles qui apparaissent dans la cohomologie $ell $ -adique lorsqu’on oublie l’action du groupe de Weil. La preuve repose sur une généralisation d’un résultat d’excision de Grosse-Klönne et de la description explicite du premier revêtement en tant que revêtement cyclique obtenu par l’auteur dans un travail précédent.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171096","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

TWISTED GAN–GROSS–PRASAD CONJECTURE FOR CERTAIN TEMPERED L-PACKETS 某些钢化L包的扭曲甘-格罗斯-普拉萨德猜想

IF 0.9 2区数学

Journal of the Institute of Mathematics of Jussieu Pub Date : 2024-05-24 DOI: 10.1017/s1474748024000197

Rui Chen, Wee Teck Gan

引用次数: 0

ARCHIMEDEAN NEWFORM THEORY FOR 的拱顶新形式理论

IF 0.9 2区数学

Journal of the Institute of Mathematics of Jussieu Pub Date : 2024-05-17 DOI: 10.1017/s1474748024000227

Peter Humphries

{"title":"ARCHIMEDEAN NEWFORM THEORY FOR","authors":"Peter Humphries","doi":"10.1017/s1474748024000227","DOIUrl":"https://doi.org/10.1017/s1474748024000227","url":null,"abstract":"\u0000 We introduce a new invariant, the conductor exponent, of a generic irreducible Casselman–Wallach representation of \u0000 \u0000 \u0000 \u0000$operatorname {mathrm {GL}}_n(F)$\u0000\u0000 \u0000 , where F is an archimedean local field, that quantifies the extent to which this representation may be ramified. We also determine a distinguished vector, the newform, occurring with multiplicity one in this representation, with the complexity of this vector measured in a natural way by the conductor exponent. Finally, we show that the newform is a test vector for \u0000 \u0000 \u0000 \u0000$operatorname {mathrm {GL}}_n times operatorname {mathrm {GL}}_n$\u0000\u0000 \u0000 and \u0000 \u0000 \u0000 \u0000$operatorname {mathrm {GL}}_n times operatorname {mathrm {GL}}_{n - 1}$\u0000\u0000 \u0000 Rankin–Selberg integrals when the second representation is unramified. This theory parallels an analogous nonarchimedean theory due to Jacquet, Piatetski-Shapiro, and Shalika; combined, this completes a global theory of newforms for automorphic representations of \u0000 \u0000 \u0000 \u0000$operatorname {mathrm {GL}}_n$\u0000\u0000 \u0000 over number fields. By-products of the proofs include new proofs of Stade’s formulæ and a new resolution of the test vector problem for archimedean Godement–Jacquet zeta integrals.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140962654","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

JMJ volume 23 issue 3 Cover and Front matter JMJ 第 23 卷第 3 期封面和封底

IF 0.9 2区数学

Journal of the Institute of Mathematics of Jussieu Pub Date : 2024-05-01 DOI: 10.1017/s1474748024000203

引用次数: 0

JMJ volume 23 issue 3 Cover and Back matter JMJ 第 23 卷第 3 期封面和封底

IF 0.9 2区数学

Journal of the Institute of Mathematics of Jussieu Pub Date : 2024-05-01 DOI: 10.1017/s1474748024000215

引用次数: 0

ADDENDUM: REAL TOPOLOGICAL HOCHSCHILD HOMOLOGY OF SCHEMES 增编：方案的实拓扑霍赫希尔德同源性

IF 0.9 2区数学

Journal of the Institute of Mathematics of Jussieu Pub Date : 2024-05-01 DOI: 10.1017/s1474748024000069

J. Hornbostel, Doosung Park

引用次数: 0

WILES DEFECT OF HECKE ALGEBRAS VIA LOCAL-GLOBAL ARGUMENTS 通过局部-全局论证的赫克代数的怀尔斯缺陷

IF 0.9 2区数学

Journal of the Institute of Mathematics of Jussieu Pub Date : 2024-04-25 DOI: 10.1017/s1474748024000021

Gebhard Böckle, Chandrashekhar B. Khare, Jeffrey Manning

{"title":"WILES DEFECT OF HECKE ALGEBRAS VIA LOCAL-GLOBAL ARGUMENTS","authors":"Gebhard Böckle, Chandrashekhar B. Khare, Jeffrey Manning","doi":"10.1017/s1474748024000021","DOIUrl":"https://doi.org/10.1017/s1474748024000021","url":null,"abstract":"In his work on modularity of elliptic curves and Fermat’s last theorem, A. Wiles introduced two measures of congruences between Galois representations and between modular forms. One measure is related to the order of a Selmer group associated to a newform $f in S_2(Gamma _0(N))$ (and closely linked to deformations of the Galois representation $rho _f$ associated to f), whilst the other measure is related to the congruence module associated to f (and is closely linked to Hecke rings and congruences between f and other newforms in $S_2(Gamma _0(N))$ ). The equality of these two measures led to isomorphisms $R={mathbf T}$ between deformation rings and Hecke rings (via a numerical criterion for isomorphisms that Wiles proved) and showed these rings to be complete intersections. We continue our study begun in [BKM21] of the Wiles defect of deformation rings and Hecke rings (at a newform f) acting on the cohomology of Shimura curves over ${mathbf Q}$ : It is defined to be the difference between these two measures of congruences. The Wiles defect thus arises from the failure of the Wiles numerical criterion at an augmentation $lambda _f:{mathbf T} to {mathcal O}$ . In situations we study here, the Taylor–Wiles–Kisin patching method gives an isomorphism <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140803590","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

KOBAYASHI-OCHIAI’S FINITENESS THEOREM FOR ORBIFOLD PAIRS OF GENERAL TYPE 一般类型轨道对的小林町有限性定理

IF 0.9 2区数学

Journal of the Institute of Mathematics of Jussieu Pub Date : 2024-04-17 DOI: 10.1017/s1474748024000094

Finn Bartsch, Ariyan Javanpeykar

引用次数: 0

ON THE DISTINCTION OF IWAHORI-SPHERICAL DISCRETE SERIES REPRESENTATIONS 关于岩崛球面离散数列表示的区别

IF 0.9 2区数学

Journal of the Institute of Mathematics of Jussieu Pub Date : 2024-04-17 DOI: 10.1017/s1474748024000185

Paul Broussous

{"title":"ON THE DISTINCTION OF IWAHORI-SPHERICAL DISCRETE SERIES REPRESENTATIONS","authors":"Paul Broussous","doi":"10.1017/s1474748024000185","DOIUrl":"https://doi.org/10.1017/s1474748024000185","url":null,"abstract":"Let $E/F$ be a quadratic unramified extension of non-archimedean local fields and $mathbb H$ a simply connected semisimple algebraic group defined and split over F. We establish general results (multiplicities, test vectors) on ${mathbb H} (F)$ -distinguished Iwahori-spherical representations of ${mathbb H} (E)$ . For discrete series Iwahori-spherical representations of ${mathbb H} (E)$ , we prove a numerical criterion of ${mathbb H} (F)$ -distinction. As an application, we classify the ${mathbb H} (F)$ -distinguished discrete series representations of ${mathbb H} (E)$ corresponding to degree $1$ characters of the Iwahori-Hecke algebra.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140609156","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