On Local Models with Special Parahoric Level Structure
On Local Models with Special Parahoric Level Structure
复制标题
具有特殊超视水平结构的局部模型
DOI：
10.1307/mmj/1260475695
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发表时间：
2008
影响因子：
0.9
通讯作者：
Kai Arzdorf
中科院分区：
文献类型：
--
作者：
Kai Arzdorf
我们考虑 Shimura 变体 PEL 类型的局部模型，其酉相似对应于 $\mathbb{Q}_p$ 的分支二次扩展作为定义群。我们研究了 $p$ 处的能级结构由一个自对偶周期晶格链的稳定剂给出的情况，这在 Bruhat-Tits 理论的意义上是特殊的。我们证明，在这些情况下，局部模型的特殊纤维是不可约的，并且是一般约约的；因此，特殊纤维被减少并且是正常的，弗罗贝尼乌斯分裂，并且只有有理奇点。此外，我们还表明，在这些情况下，局部模型包含一个与仿射空间同构的开子集。
We consider the local model of a Shimura variety of PEL type, with the unitary similitudes corresponding to a ramified quadratic extension of $\mathbb{Q}_p$ as defining group. We examine the cases where the level structure at $p$ is given by a parahoric that is the stabilizer of a selfdual periodic lattice chain and that is special in the sense of Bruhat--Tits theory. We prove that in these cases the special fiber of the local model is irreducible and generically reduced; consequently, the special fiber is reduced and is normal, Frobenius split, and with only rational singularities. In addition, we show that in these cases the local model contains an open subset that is isomorphic to affine space.