Supersingular K3 surfaces are unirational

I show that supersingular K3 surfaces in positive characteristic are related by purely inseparable isogenies. As an application, I deduce that supersingular K3 surfaces are unirational, which confirms conjectures Artin, Rudakov, Shafarevich, and Shioda. The main ingredient in the proof is to use the formal Brauer group of a Jacobian elliptically fibered supersingular K3 surface to construct a family of "moving torsors" under this fibration that eventually related supersingular K3 surfaces of different Artin invariants by purely inseparable isogenies. If time permits, I will also explain how these moving torsors exhibit Ogus' moduli space of supersingular K3 crystals as an iterated projective bundle over a finite field.