LEFSCHETZ NUMBER FORMULA FOR SHIMURA VARIETIES OF HODGE TYPE

被引：0

作者：

Lee, Dong Uk ^{[1
]}

机构：

[1] Chungnam Natl Univ, Math Sci Res Inst, 34134,99 Daehang Ro, Daejeon, Chungcheongnam, South Korea

来源：

ASIAN JOURNAL OF MATHEMATICS | 2024年 / 28卷 / 01期

关键词：

Shimura varieties; Lefschetz number formula; Langlands-Kottwitz method; VERDIER TRACE FORMULA; ISOGENY CLASSES; ISOCRYSTALS; REDUCTION; POINTS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For any Shimura variety of Hodge type with hyperspecial level at a prime p and automorphic lisse sheaf on it, we prove a formula, conjectured by Kottwitz [Kot90], for the Lefschetz numbers of Frobenius-twisted Hecke correspondences acting on the compactly supported & eacute;tale cohomology. Our proof is an adaptation of the arguments of Langlands and Rapoport [LR87] of deriving the Kottwitz's formula from their conjectural description of the set of mod-p points of Shimura variety (Langlands-Rapoport conjecture), but replaces their Galois gerb theoretic arguments by more standard group-theoretic ones, using Kisin's geometric work [Kis17]. We also prove a generalization of Honda-Tate theorem in the context of Shimura varieties and fix an error in the Kisin's work. We do not assume that the derived group is simply connected

引用

页码：103 / 196

页数：94