$P$-alcoves and nonemptiness of affine Deligne-Lusztig varieties

Ulrich Gortz University of Duisburg-Essen Xuhua He University of Maryland Sian Nie Chinese Academy of Sciences

Arithmetic Geometry and Commutative Algebra mathscidoc:1803.07002

Ann. Sci. Ec. Norm. Super, 48, 647-665, 2015
We study affine Deligne-Lusztig varieties in the affine flag manifold of an algebraic group, and in particular the question, which affine Deligne-Lusztig varieties are non-empty. Under mild assumptions on the group, we provide a complete answer to this question in terms of the underlying affine root system. In particular, this proves the corresponding conjecture for split groups stated in \cite{GHKR2}. The question of non-emptiness of affine Deligne-Lusztig varieties is closely related to the relationship between certain natural stratifications of moduli spaces of abelian varieties in positive characteristic.
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  title={$P$-alcoves and nonemptiness of affine Deligne-Lusztig varieties},
  author={Ulrich Gortz, Xuhua He, and Sian Nie},
  booktitle={Ann. Sci. Ec. Norm. Super},
Ulrich Gortz, Xuhua He, and Sian Nie. $P$-alcoves and nonemptiness of affine Deligne-Lusztig varieties. 2015. Vol. 48. In Ann. Sci. Ec. Norm. Super. pp.647-665. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180321221309171029987.
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