Oort's amalgamated-sum conjecture for Newton polygons on the Torelli locus

For i=1,2i=1,2, let giZ1g_i\in\mathbb{Z}_{\ge 1}, and let νi\nu_i be a symmetric Newton polygon appearing on the open Torelli locus Tgi\mathcal{T}_{g_i}^{\circ}. Write

g=g1+g2.g=g_1+g_2.

Let ν\nu be the amalgamate sum of ν1\nu_1 and ν2\nu_2. Oort's conjecture. The Newton polygon ν\nu appears on the open Torelli locus Tg\mathcal{T}_g^{\circ}.

The conjecture predicts that Newton polygons occurring for Jacobians of smooth curves can be combined under addition of the genera. It is attributed to Oort; the source does not state whether it has been resolved.

Sources & referencesView supporting material

Primary source

Wanlin Li, Elena Mantovan, Rachel Pries and Yunqing Tang, “Newton polygon stratification of the Torelli locus in PEL-type Shimura varieties”, arXiv:1811.00604 (2019).

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