Prescribing Newton polygons and a-numbers

Determine, within each fixed p-rank stratum, which Newton polygons and a-numbers can occur for an Artin–Schreier curve X defined over the prime field with full geometric automorphism group Aut(X)≅C_p, and characterize the genera admitting a supersingular such curve.

Background

The paper prescribes genus and p-rank while constructing Artin–Schreier curves with no automorphisms beyond the deck group C_p. It does not address finer invariants of the Jacobian or p-divisible group, such as the Newton polygon or the a-number.

The proposed problem asks whether these additional arithmetic invariants can simultaneously be prescribed within a fixed p-rank stratum under the same minimal-automorphism condition. The paper gives supersingularity as a concrete case, asking which genera support a supersingular Artin–Schreier curve with full geometric automorphism group C_p.

References

Within a fixed $p$-rank stratum, can one also prescribe the Newton polygon, or the $a$-number, of an Artin--Schreier curve $X/$ with $Aut_{}(X)\cong C_p$? For instance, which genera admit a supersingular such curve?

— Artin-Schreier curves of prescribed p-rank without extra automorphisms  (2610.13279 - Tafazolian et al., 9 Oct 2026) in Section 6, final Question environment (Summary of the models and further remarks)