非紧算术流形的自同构LEFSCHETZ性质

IF 1.1 2区数学 Q1 MATHEMATICS Journal of the Institute of Mathematics of Jussieu Pub Date : 2021-10-18 DOI:10.1017/S1474748021000499

A. Nair, Ankit Rai

{"title":"非紧算术流形的自同构LEFSCHETZ性质","authors":"A. Nair, Ankit Rai","doi":"10.1017/S1474748021000499","DOIUrl":null,"url":null,"abstract":"Abstract We prove the injectivity of Oda-type restriction maps for the cohomology of noncompact congruence quotients of symmetric spaces. This includes results for restriction between (1) congruence real hyperbolic manifolds, (2) congruence complex hyperbolic manifolds, and (3) orthogonal Shimura varieties. These results generalize results for compact congruence quotients by Bergeron and Clozel [Quelques conséquences des travaux d’Arthur pour le spectre et la topologie des variétés hyperboliques, Invent. Math. 192 (2013), 505–532] and Venkataramana [Cohomology of compact locally symmetric spaces, Compos. Math. 125 (2001), 221–253]. The proofs combine techniques of mixed Hodge theory and methods involving automorphic forms.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":"22 1","pages":"1655 - 1702"},"PeriodicalIF":1.1000,"publicationDate":"2021-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"AUTOMORPHIC LEFSCHETZ PROPERTIES FOR NONCOMPACT ARITHMETIC MANIFOLDS\",\"authors\":\"A. Nair, Ankit Rai\",\"doi\":\"10.1017/S1474748021000499\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We prove the injectivity of Oda-type restriction maps for the cohomology of noncompact congruence quotients of symmetric spaces. This includes results for restriction between (1) congruence real hyperbolic manifolds, (2) congruence complex hyperbolic manifolds, and (3) orthogonal Shimura varieties. These results generalize results for compact congruence quotients by Bergeron and Clozel [Quelques conséquences des travaux d’Arthur pour le spectre et la topologie des variétés hyperboliques, Invent. Math. 192 (2013), 505–532] and Venkataramana [Cohomology of compact locally symmetric spaces, Compos. Math. 125 (2001), 221–253]. The proofs combine techniques of mixed Hodge theory and methods involving automorphic forms.\",\"PeriodicalId\":50002,\"journal\":{\"name\":\"Journal of the Institute of Mathematics of Jussieu\",\"volume\":\"22 1\",\"pages\":\"1655 - 1702\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2021-10-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Institute of Mathematics of Jussieu\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/S1474748021000499\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Institute of Mathematics of Jussieu","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/S1474748021000499","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

摘要我们证明了对称空间的非紧同余商的上同调的Oda型限制映射的内射性。这包括了（1）同余实双曲流形、（2）同余复双曲流形和（3）正交Shimura变种之间的约束结果。这些结果推广了Bergeron和Clozel[Quelques conséSequences des travaux d’Arthur pour le spectre et la topologie des variétés双曲线，Invent.Math.192（2013），505–532]和Venkataramana[紧致局部对称空间的同调，Compos.Math.125（2001），221–253]关于紧致同调商的结果。这些证明结合了混合Hodge理论的技术和涉及自同构形式的方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

AUTOMORPHIC LEFSCHETZ PROPERTIES FOR NONCOMPACT ARITHMETIC MANIFOLDS

Abstract We prove the injectivity of Oda-type restriction maps for the cohomology of noncompact congruence quotients of symmetric spaces. This includes results for restriction between (1) congruence real hyperbolic manifolds, (2) congruence complex hyperbolic manifolds, and (3) orthogonal Shimura varieties. These results generalize results for compact congruence quotients by Bergeron and Clozel [Quelques conséquences des travaux d’Arthur pour le spectre et la topologie des variétés hyperboliques, Invent. Math. 192 (2013), 505–532] and Venkataramana [Cohomology of compact locally symmetric spaces, Compos. Math. 125 (2001), 221–253]. The proofs combine techniques of mixed Hodge theory and methods involving automorphic forms.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of the Institute of Mathematics of Jussieu 数学-数学

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of the Institute of Mathematics of Jussieu publishes original research papers in any branch of pure mathematics; papers in logic and applied mathematics will also be considered, particularly when they have direct connections with pure mathematics. Its policy is to feature a wide variety of research areas and it welcomes the submission of papers from all parts of the world. Selection for publication is on the basis of reports from specialist referees commissioned by the Editors.

期刊最新文献

EXCEPTIONAL SIMPLE REAL LIE ALGEBRAS AND VIA CONTACTIFICATIONS COHOMOLOGIE DE DE RHAM DU REVÊTEMENT MODÉRÉ DE L’ESPACE DE DRINFELD TWISTED GAN–GROSS–PRASAD CONJECTURE FOR CERTAIN TEMPERED L-PACKETS WILES DEFECT OF HECKE ALGEBRAS VIA LOCAL-GLOBAL ARGUMENTS KOBAYASHI-OCHIAI’S FINITENESS THEOREM FOR ORBIFOLD PAIRS OF GENERAL TYPE