2026/06/15 by Emerald Andrews, Deewang Bhamidipati, Maria Fox +3
Mathematics · #math.NT
In this paper, we give a complete classification of indecomposable Ekedahl--Oort strata of Shimura varieties associated to the unitary group GU(a, b) over an odd inert prime. We show that each indecomposable stratum is one of four types: unitary unicycle, unitary bicycle, Serre unicycle, or Serre bicycle; the latter two types are named for a tensor construction of abelian varieties developed by Serre. We provide an algorithm that translates the description of a stratum in terms of words in the alphabet \f,v\ to the corresponding Weyl group coset representative. Finally, using a p-adic lift, we construct a `tautological' point in each Ekedahl--Oort stratum, and compute its Newton polygon. As an application, we show that the indecomposable Ekedahl--Oort strata corresponding to unitary unicycles and Serre unicycles always intersect the supersingular locus.