Boundary cohomology of Shimura varieties. I: Coherent cohomology on toroidal compactifications
Boundary cohomology of Shimura varieties. I: Coherent cohomology on toroidal compactifications
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Shimura 簇的边界上同调。
DOI：
10.24033/asens.1695
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发表时间：
1994
影响因子：
1.9
通讯作者：
S. Zucker
中科院分区：
文献类型：
--
作者：
M. Harris;S. Zucker
研究了自守向量丛的相干上同调，仅限于与极大有理抛物子群相关的志村簇的环形边界层。上同调的计算附在边界组件的志村品种的相干上同调。主要结果是关于一个整体相干上同调类对与极大抛物P相关的边界层的限制;证明了，根据具有增长条件的Dolbeault上同调，通过沿P的幂幺根取常数项沿着给出了这个限制。这个结果被用来证明某些非全纯的，绝对收敛的Eisenstein级数定义了有理整体（凝聚）上同调类。主要的技术建设是一个比较之间的（单纯）Dolbeault复杂的复杂的环面嵌入和（单纯）德拉姆复杂的“真实的部分”。
We study the coherent cohomology of automorphic vector bundles, restricted to the toroidal boundary strata of Shimura varieties associated to maximal rational parabolic subgroups. The cohomology is computed in terms of coherent cohomology of the Shimura varieties attached to the boundary components. The main result concerns the restriction of a global coherent cohomology class to the boundary stratum associated with the maximal parabolic P; it is shown that, in terms of Dolbeault cohomology with growth conditions, this restriction is given by taking the constant term along the unipotent radical of P. This result is used to show that certain non-holomorphic, absolutely convergent Eisenstein series define rational global (coherent) cohomology classes. The main technical construction is a comparison between the (simplicial) Dolbeault complex associated to a complex torus embedding and the (simplicial) de Rham complex associated to its "real part".