Artin's Frobenius-pullback conjecture for supersingular elliptic K3 surfaces

Let XX be a supersingular K3 surface in characteristic 22, equipped with an elliptic fibration. A rational elliptic surface is a rational surface with an elliptic fibration, and Frobenius pullback means pullback of the fibration along the absolute Frobenius of the base.

Artin's Frobenius-pullback conjecture. The elliptic fibration on XX arises via Frobenius pullback from a rational elliptic surface.

This conjecture is presented as a geometric explanation for the supersingularity and unirationality conjectures above. The source gives no resolution status for it.

Sources & referencesView supporting material

Primary source

Hiroyuki Ito and Christian Liedtke, “Elliptic K3 surfaces with p^n-torsion sections”, arXiv:1003.0144 (2011).

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