Abstract: If a Kummer surface over a discretely valued field of characteristic zero has good reduction, then it comes from an abelian surface with good reduction.The converse holds if the residual characteristic is not 2. In a joint work with Chris Lazda we obtain a necessary and sufficient condition for good reduction of Kummer surfaces attached to abelian surfaces with good, non-supersingular reduction in residual characteristic 2. We also give a similar criterion for ‘twisted’ Kummer surfaces attached to 2-coverings of abelian surfaces. The supersingular case is very interesting but seems to be completely open.
Ref: C. Lazda and A. Skorobogatov, Reduction of Kummer surfaces modulo 2 in the non-supersingular case
