Counting Points on Igusa Varieties of Hodge Type
Number Theory
2022-03-04 v1
Abstract
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.
Cite
@article{arxiv.2203.01448,
title = {Counting Points on Igusa Varieties of Hodge Type},
author = {Sander Mack-Crane},
journal= {arXiv preprint arXiv:2203.01448},
year = {2022}
}