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Supersingular K3 Surfaces are Unirational

Christian Liedtke

Number 26
Author Christian Liedtke
Year 2013

We show that supersingular K3 surfaces in characteristic p5 are related by purely inseparable isogenies. This implies that they are unirational, which proves conjectures of Artin, Rudakov, Shafarevich, and Shioda. As a byproduct, we exhibit the moduli space of rigidified K3 crystals as an iterated P1-bundle over Fp2. To complete the picture, we also establish Shioda-Inose type isogeny theorems for K3 surfaces with Picard rank ρ19 in positive characteristic.

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