arXiv subjects

Emerald Andrews

Publications and source records attributed to Emerald Andrews.

4 recordsLinked to original sources

arXiv2026

On the classification of indecomposable Ekedahl-Oort strata in unitary Shimura varieties, and related Newton polygons

In this paper, we give a complete classification of indecomposable Ekedahl--Oort strata of Shimura varieties associated to the unitary group $\mathsf{GU}(a, b)$ 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 $\{\texttt{f},\texttt{v}\}$ 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.

math.NT↗

arXiv2025

The Ekedahl-Oort and Newton stratification of the $\mathsf{GU}(3,2)$ Shimura variety

This paper concerns the characteristic-$p$ fibers of $\mathsf{GU}(3,2)$ Shimura varieties. Such Shimura varieties parametrize abelian varieties in characteristic $p$ of dimension $5$ with an action of signature $(3,2)$ by an order in an imaginary quadratic field in which $p$ is inert. We completely describe the interaction of two stratifications of these Shimura varieties: the Ekedahl-Oort stratification, based on the isomorphism class of the $p$-torsion subgroup scheme, and the Newton stratification, based on the isogeny class of the $p$-divisible group. We identify which Ekedahl-Oort and Newton strata intersect.

math.NT↗

arXiv2025

Traverso's Isogeny Conjecture for Some Unitary p-Divisible Groups

The isogeny cutoff of a $p$-divisible group $X$ (defined over an algebraically closed field of characteristic $p$) measures the amount of $p$-torsion necessary to determine its isogeny class. The minimal height of $X$ measures its distance to the closest minimal $p$-divisible group (in the sense of Oort). In this paper, we study these invariants for supersingular unitary $p$-divisible groups of signature $(a,b)$. We provide a complete description of the possible minimal heights. As an application, we establish bounds on the isogeny cutoffs for these $p$-divisible groups. Finally, we rephrase our results in the language of the $\mathrm{BT}_m$ stratifications of unitary Shimura varieties of signature $(a,b)$.

math.NT↗

arXiv2024

Ekedahl-Oort strata in the $\mathsf{GU}(q-2,2)$ Shimura variety

This paper concerns the characteristic-$p$ fibers of $\mathsf{GU}(q-2,2)$ Shimura varieties, which classify abelian varieties with additional structure. These Shimura varieties admit two stratifications of interest: the Ekedahl-Oort stratification, based on the isomorphism class of the $p$-torsion subgroup scheme, and the Newton stratification, based on the isogeny class of the $p$-divisible group. In this paper, we present several novel techniques that give a better understanding of the Ekedahl-Oort stratification and of the interaction between the two stratifications for a general signature $(q-2,2)$.

math.NT↗