number 1 in detail. Kummer surfaces If the characteristic p is greater than 2, showed that every K3 surface S with Picard number 22 and Artin invariant at most 2 is a Kummer surface, meaning the minimal resolution of the quotient of an abelian surface A by the mapping x ↦ − x. More precisely, A is a supersingular abelian surface, isogenous to the product of two supersingular elliptic curves. See also K3 surface Tate conjecture Notes References Algebraic surfaces