Oort's amalgamation conjecture for Newton polygons of curves

Let pp be a prime and let CC and CC' be smooth proper irreducible curves of genera gg and gg', with Newton polygons PP and PP', respectively. A Newton polygon is determined by its multiset of slopes, counted with multiplicity; the amalgamation of PP and PP' is the Newton polygon whose slopes are the disjoint union of the slopes of PP and PP'. Oort's amalgamation conjecture. There exists a smooth proper irreducible curve CC” of genus g+gg+g' whose Newton polygon is the amalgamation of PP and PP'. This conjecture gives guidance on which Newton polygons can occur for curves in characteristic pp: it predicts that combining the Newton polygons of two curves can be realized by a single curve of the summed genus. The paper cites Oort's formulation as Conjecture 8.5.7; the source provides no resolution status.

Sources & referencesView supporting material

Primary source

Joe Kramer-Miller, “Some unlikely intersections between the Torelli locus and Newton strata in A_g”, arXiv:2006.04927 (2020).

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