Irreducible components of affine Deligne-Lusztig varieties

Abstract

By extending the method of semi-modules developed by de Jong, Oort, Viehmann and Hamacher, we introduce a stratification for the affne Deligne-Lusztig variety (in the affne Grassmannian) attached to attached to a minuscule cocharacter and a basic element. As an application, we complete the proof of a conjecture on the irreducible components of affne Deligne-Lusztig varieties, due to Miaofen Chen and Xinwen Zhu.

Substantially overlap with arXiv:1802.04579. An explicit construction of irreducible components is added. The proof of the conjecture by Chen and Zhu is completed