Stratifications of affine Deligne-Lusztig varieties

Görtz, Ulrich

doi:10.1090/tran/7715

Stratifications of affine Deligne-Lusztig varieties
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by Ulrich Görtz PDF

Trans. Amer. Math. Soc. 372 (2019), 4675-4699

Abstract:

Affine Deligne-Lusztig varieties are analogues of Deligne-Lusztig varieties in the context of affine flag varieties and affine Grassmannians. They are closely related to moduli spaces of $p$-divisible groups in positive characteristic and thus to arithmetic properties of Shimura varieties.

We compare stratifications of affine Deligne-Lusztig varieties attached to a basic element $b$. In particular, we show that the stratification defined by Chen and Viehmann using the relative position to elements of the group $\mathbb {J}_b$, the $\sigma$-centralizer of $b$, coincides with the Bruhat-Tits stratification in all cases of Coxeter type, as defined by X. He and the author.

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