论文标题
签名$（1，n-1）$的基本未受到的pel rapoport-zink统一空间的共同学
Cohomology of the basic unramified PEL unitary Rapoport-Zink space of signature $(1,n-1)$
论文作者
论文摘要
在本文中，我们研究了最大水平的签名$（1，n-1）$的单一未受到的pel Rapoport-Zink空间的共同体。我们的方法围绕着与特殊纤维中封闭的bruhat-tits地层的分析管相关的光谱序列，该序列是由Vollaard和Wedhorn构建的。这些地层的共同体学是在先前的论文中计算出来的。这种频谱序列使我们能够证明弗罗贝尼乌斯作用的半透明性以及总体上的同种学的不可接受。通过$ p $ - 亚种均匀化，我们将Rapoport-Zink空间的共同学与Shimura品种的超词基因座的共同体相关联，没有$ p $的水平。在情况下，$ n = 3 $或$ 4 $，我们就自动形式表示，对超级基因座的共同体进行了完整的描述。
In this paper, we study the cohomology of the unitary unramified PEL Rapoport-Zink space of signature $(1,n-1)$ at maximal level. Our method revolves around the spectral sequence associated to the open cover by the analytical tubes of the closed Bruhat-Tits strata in the special fiber, which were constructed by Vollaard and Wedhorn. The cohomology of these strata, which are isomorphic to generalized Deligne-Lusztig varieties, has been computed in a previous paper. This spectral sequence allows us to prove the semisimplicity of the Frobenius action and the non-admissibility of the cohomology in general. Via $p$-adic uniformization, we relate the cohomology of the Rapoport-Zink space to the cohomology of the supersingular locus of a Shimura variety with no level at $p$. In the case $n=3$ or $4$, we give a complete description of the cohomology of the supersingular locus in terms of automorphic representations.
