非紧算术流形的自同构LEFSCHETZ性质

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-10-18 DOI:10.1017/S1474748021000499

A. Nair, Ankit Rai

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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。

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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.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.