ON THE COHOMOLOGY GROUPS OF LOCAL SYSTEMS OVER HILBERT MODULAR VARIETIES VIA HIGGS BUNDLES

被引：0

作者：

Mueller-Stach, Stefan ^{[1
]}

Sheng, Mao ^{[2
]}

Ye, Xuanming ^{[3
]}

Zuo, Kang ^{[1
]}

机构：

[1] Johannes Gutenberg Univ Mainz, D-55099 Mainz, Germany

[2] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Peoples R China

[3] Sun Yat Sen Univ, Sch Math & Computat Sci, Guangzhou 510275, Guangdong, Peoples R China

来源：

AMERICAN JOURNAL OF MATHEMATICS | 2015年 / 137卷 / 01期

基金：

中国国家自然科学基金;

关键词：

L2; CO-HOMOLOGY; SHIMURA VARIETIES; HODGE; L2-COHOMOLOGY; PRODUCT;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X be a Hilbert modular variety and V a non-trivial local system over X with infinite monodromy. In this paper we study Saito's mixed Hodge structure (MHS) on the cohomology group H-k (X, V) using the method of Higgs bundles. Among other results we prove the Eichler-Shimura isomorphism, give a dimension formula for the Hodge numbers and show that the mixed Hodge structure is split over R. These results are analogous to the work of Y. Matsushima and G. Shimura in the cocompact case and complement the results of E. Frietag for constant coefficients.

引用

页码：1 / 35

页数：35

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