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arXiv · 1408.5838

Kottwitz-Rapoport conjecture on unions of affine Deligne-Lusztig varieties

Xuhua He
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Abstract

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 any tamely ramified 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.

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Xuhua He. 2014-08-25. Kottwitz-Rapoport conjecture on unions of affine Deligne-Lusztig varieties. https://arxiv.org/abs/1408.5838

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