Simply connected surfaces of general type in positive characteristic via deformation theory

Algebraically simply connected surfaces of general type with p_g=q=0 and 1\le K^2\le 4 in positive characteristic (with one exception in K^2=4) are presented by using a Q-Gorenstein smoothing of two-dimensional toric singularities, a generalization of Lee-Park's construction in the field of complex numbers to the positive characteristic case, and Grothendieck's specialization theorem for the fundamental group.