分枝素数上GU(2,2)的Shimura变异的超奇异座

IF 0.6 4区数学 Q3 MATHEMATICS

International Journal of Mathematics Pub Date : 2023-11-07 DOI:10.1142/s0129167x23500945

Yasuhiro Oki

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引用次数: 0

摘要

研究了具有特殊极大旁水平的分枝奇素数上GU(2,2)的Shimura型Rapoport-Zink积分模型的超奇异轨迹的结构。证明了超奇异轨迹等于两个基本轨迹的不相交并，其中一个包含在平面轨迹中，而另一个不包含在平面轨迹中。我们还明确地描述了基本基因座的结构。更准确地说，前者是纯二维的，每个不可约分量都与费马曲面有关。另一方面，后者是纯粹的[公式:见文本]维的，每一个不可约的分量都与投影线有关。

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On the Supersingular Locus of the Shimura Variety for GU(2,2) over a Ramified Prime

We study the structure of the supersingular locus of the Rapoport–Zink integral model of the Shimura variety for GU(2,2) over a ramified odd prime with the special maximal parahoric level. We prove that the supersingular locus equals the disjoint union of two basic loci, one of which is contained in the flat locus, and the other is not. We also describe explicitly the structure of the basic loci. More precisely, the former one is purely 2-dimensional, and each irreducible component is birational to the Fermat surface. On the other hand, the latter one is purely [Formula: see text]-dimensional, and each irreducible component is birational to the projective line.

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来源期刊

International Journal of Mathematics 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： The International Journal of Mathematics publishes original papers in mathematics in general, but giving a preference to those in the areas of mathematics represented by the editorial board. The journal has been published monthly except in June and December to bring out new results without delay. Occasionally, expository papers of exceptional value may also be published. The first issue appeared in March 1990.