On supersingular loci of Shimura varieties for quaternionic unitary groups of degree 2
On supersingular loci of Shimura varieties for quaternionic unitary groups of degree 2
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关于2次四元酉群Shimura簇的超奇异位点
DOI：
10.1007/s00229-020-01265-4
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发表时间：
2021
影响因子：
0.6
通讯作者：
Oki Yasuhiro
中科院分区：
文献类型：
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作者：
Yutaka Iwasaki;Koichi Kitahara;Kaoru Kimura;岩崎祐昂;Miyakawa K. et al. (including Fukui A.);岩崎祐昂;Oki Yasuhiro
本文描述了分歧奇素数p上2次四元酉相似群的Shimura簇的超奇异轨迹的结构，如果水平atp由一个特殊的极大紧开子群给出.更确切地说，我们表明，这样的轨迹是纯粹的2维，和每个不可约的组件是双理性的费马曲面。此外，我们有一个估计的数量的连通和不可约的组件。为了证明这些断言，我们完全确定了具有特殊仿射水平的2度四元数酉相似群的Rapoport-Zink空间的底层约化方案的结构。我们证明了这样的计划是纯2维的，每一个不可约的组件是同构的费马曲面。我们还确定了它的连通分支，不可约分支和它们的交叉行为的Bruhat-Tits建立。此外，在极小情形下，我们还计算了在超特殊水平下的非分歧的Rapoport-Zink空间中嵌入的GGP圈的交重数.
We describe the structure of the supersingular locus of a Shimura variety for a quaternionic unitary similitude group of degree 2 over a ramified odd primepif the level atpis given by a special maximal compact open subgroup. More precisely, we show that such a locus is purely 2-dimensional, and every irreducible component is birational to the Fermat surface. Furthermore, we have an estimation of the numbers of connected and irreducible components. To prove these assertions, we completely determine the structure of the underlying reduced scheme of the Rapoport–Zink space for the quaternionic unitary similitude group of degree 2, with a special parahoric level. We prove that such a scheme is purely 2-dimensional, and every irreducible component is isomorphic to the Fermat surface. We also determine its connected components, irreducible components and their intersection behaviors by means of the Bruhat–Tits building of. In addition, we compute the intersection multiplicity of the GGP cycles associated to an embedding of the considering Rapoport–Zink space into the Rapoport–Zink space for the unramifiedwith hyperspecial level for the minuscule case.