Siegel模簇与$\PGL_{2g+1}$的Eisenstein上同调
Siegel Modular Varieties and the Eisenstein Cohomology of $\PGL_{2g+1}$
摘要：
我们使用扭曲的拓扑轨迹公式在较早的文件，以了解提升从辛到一般线性群。我们进一步详细地分析了从$\SP_{2g}$到$\PGL_{2g+1}$在基域$\Q$上的提升，并且我们得到了这个提升对于$\SP_{2g}$的$L^2$上同调（这与附在$\GSp_{2g}$上的Shimura簇的交上同调有关）的图像的描述，该图像是根据一般线性群的Eisenstein上同调的，其构建成分是Levi群的尖点表示。这种描述可以用来理解辛群的内窥镜和CAP表示。
英文摘要：
We use the twisted topological trace formula developed in an earlier paper to understand liftings from symplectic to general linear groups. We analyse the lift from $\SP_{2g}$ to $\PGL_{2g+1}$ over the ground field $\Q$ in further detail, and we get a description of the image of this lift for the $L^2$ cohomology of $\SP_{2g}$ (which is related to the intersection cohomology of the Shimura variety attached to $\GSp_{2g}$) in terms of the Eisenstein cohomology of the general linear group, whose building constituents are cuspidal representations of Levi groups. This description may be used to understand endoscopic and CAP-representations of the symplectic group.
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