Christian Liedtke

Title: Supersingular K3 surfaces are unirational

Abstract: 
We show that supersingular K3 surfaces are related by purely 
inseparable isogenies. Using work of Shioda, we deduce that 
they are unirational, which confirms conjectures of 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 
relates supersingular K3 surfaces of different Artin invariants 
by purely inseparable isogenies.