Oort's direct-sum conjecture for Newton polygons

Let pp be a prime, and let ξ1\xi_1 and ξ2\xi_2 be Newton polygons that are realized in characteristic pp. Oort's direct-sum conjecture. Then ξ1ξ2\xi_1 \oplus \xi_2 is realized in characteristic pp. This conjecture concerns whether realizability of Newton polygons in a fixed characteristic is preserved under direct sum. The supplied context says it is an expectation of Oort and that the paper proves several results about it, but does not state that the conjecture itself is resolved.

Sources & referencesView supporting material

Primary source

Darren Schmidt, “Ekedahl-Oort Types and Newton Polygons of Abelian Covers of P^1 Branched at Three Points”, arXiv:2602.07693 (2026).

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