Oort's amalgamation conjecture for Newton polygons of curves
Oort's amalgamation conjecture for Newton polygons of curves
Let be a prime and let and be smooth proper irreducible curves of genera and , with Newton polygons and , respectively. A Newton polygon is determined by its multiset of slopes, counted with multiplicity; the amalgamation of and is the Newton polygon whose slopes are the disjoint union of the slopes of and . Oort's amalgamation conjecture. There exists a smooth proper irreducible curve of genus whose Newton polygon is the amalgamation of and . This conjecture gives guidance on which Newton polygons can occur for curves in characteristic : 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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