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

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For i=1,2i=1,2, let gi∈Z≥1g_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.

References

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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