# MathSciDoc: An Archive for Mathematician ∫

#### Arithmetic Geometry and Commutative Algebramathscidoc:1803.07004

Ann. Sci. Ecole Norm. Sup., 49, 1125-1141, 2016
In this paper, we prove a conjecture of Kottwitz and Rapoport on a union of (generalized) affine Deligne-Lusztig varieties $X(\mu, b)_J$ for a $p$-adic group $G$ and its parahoric subgroup $P_J$. We show that $X(\mu, b)_J \neq \emptyset$ if and only if the group-theoretic version of Mazur's inequality is satisfied. In the process, we obtain a generalization of Grothendieck's conjecture on the closure relation of $\s$-conjugacy classes of a twisted loop group.
Shimura varieties, affine Deligne-Lusztig varieties, Newton strata
@inproceedings{xuhua2016kottwitz-rapoport,
title={Kottwitz-Rapoport conjecture on unions of affine Deligne-Lusztig varieties},
author={Xuhua He},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180321233821992833990},
booktitle={Ann. Sci. Ecole Norm. Sup.},
volume={49},
pages={1125-1141},
year={2016},
}

Xuhua He. Kottwitz-Rapoport conjecture on unions of affine Deligne-Lusztig varieties. 2016. Vol. 49. In Ann. Sci. Ecole Norm. Sup.. pp.1125-1141. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180321233821992833990.