Geodesic
Geometric and homological properties of affine Deligne-Lusztig varieties
Xuhua He1
1 The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Annals of mathematics, Tome 179 (2014) no. 1, pp. 367-404.

Voir la notice de l'article provenant de la source Annals of Mathematics website

This paper studies affine Deligne-Lusztig varieties $X_{\tilde w}(b)$ in the affine flag variety of a quasi-split tamely ramified group. We describe the geometric structure of $X_{\tilde w}(b)$ for a minimal length element $\tilde w$ in the conjugacy class of an extended affine Weyl group. We then provide a reduction method that relates the structure of $X_{\tilde w}(b)$ for arbitrary elements $\tilde w$ in the extended affine Weyl group to those associated with minimal length elements. Based on this reduction, we establish a connection between the dimension of affine Deligne-Lusztig varieties and the degree of the class polynomial of affine Hecke algebras. As a consequence, we prove a conjecture of Görtz, Haines, Kottwitz and Reuman.
DOI : 10.4007/annals.2014.179.1.6

Xuhua He 1

1 The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong 
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Xuhua He. Geometric and homological properties of affine Deligne-Lusztig varieties. Annals of mathematics, Tome 179 (2014) no. 1, pp. 367-404. doi : 10.4007/annals.2014.179.1.6. http://geodesic.mathdoc.fr/articles/10.4007/annals.2014.179.1.6/

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