Stabilizers of irreducible components of affine Deligne--Lusztig varieties

Rong Zhou; Xuhua He; Yihang Zhu

REVIEW

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2109.02594 v1 pith:PQSGAPTV submitted 2021-09-06 math.AG math.NT

Stabilizers of irreducible components of affine Deligne--Lusztig varieties

Xuhua He , Rong Zhou , Yihang Zhu This is my paper

classification math.AG math.NT

keywords affinecomponentsirreduciblevarietiesdeligne--lusztigtop-dimensionalactionapplication

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

0 comments

read the original abstract

We study the $J_b(F)$-action on the set of top-dimensional irreducible components of affine Deligne--Lusztig varieties in the affine Grassmannian. We show that the stabilizer of any such component is a parahoric subgroup of $J_b(F)$ of maximal volume, verifying a conjecture of X.~Zhu. As an application, we give a description of the set of top-dimensional irreducible components in the basic locus of Shimura varieties.

Stabilizers of irreducible components of affine Deligne--Lusztig varieties

discussion (0)