论文标题
Igusa类型的Igusa品种的计数点
Counting Points on Igusa Varieties of Hodge Type
论文作者
论文摘要
Igusa品种是对Shimura品种的特殊纤维研究中出现的代数品种，并通过Langlands-Kottwitz风格点数计数配方在PEL类型的情况下通过Langlands-Kottwitz样式计数公式证明了Langlands计划中的许多应用。 在本文中，我们制定并证明了兰格兰斯（Langlands-Ropoport）的类似物构想霍奇类型的Igusa品种，并在Shimura品种的情况下建立了Kisin的作品。然后，我们使用这些点的描述来得出Hodge类型Igusa品种的点计数公式，通过借鉴Kisin-Shin-Zhu的技术来概括Shin的pel类型的Fomula。
Igusa varieties are algebraic varieties that arise in the study of special fibers of Shimura varieties, and have demonstrated many applications in the Langlands program via a Langlands-Kottwitz style point-counting formula due to Shin in the case of PEL type. In this paper we formulate and prove an analogue of the Langlands-Rapoport conjecture for Igusa varieties of Hodge type, building off the work of Kisin in the case of Shimura varieties. We then use this description of the points to derive a point-counting formula for Igusa varieties of Hodge type, generalizing the fomula in PEL type of Shin, by drawing on the techniques of Kisin-Shin-Zhu.
