2022/03/02 by Sander Mack-Crane, Mack-Crane, Sander
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.2203.01448
arxiv created 2022/03/02 · openalex publication_date 2022/03/02 · arxiv updated 2022/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.