$P$-alcoves and nonemptiness of affine Deligne-Lusztig varieties
By Ulrich Goertz, Xuhua He, S. Nie. 2012
48 citations recorded by the source corpus.
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 G\"ortz et al. (2010). 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.
Subfields: Algebra and Number Theory, Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/6f6c2befc741cd92d39eab74b1ac9fea8dc78010
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In Algebra and Number Theory
In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- GEOMETRIC AND HOMOLOGICAL PROPERTIES OF AFFINE DELIGNE-LUSZTIG VARIETIES (2012, methodology): “We recall the notation of ( J, w, δ )-alcoves in [6, 3.3], which generalizes the notation of P -alcoves introduced in [8].”