On Superspecial Abelian Surfaces Over Finite Fields

Let Sp₂（F_q）be the set of isomorphism classes of superspecial abelian surfaces over a finite field F_q,where F_qis of even degree over the prime field F_pof characteristic p∈{2,3,5}.Use Galois cohomology,we reduce the problem of finding isomorphism classes of superspecial abelian varieties over a finite filed to the problem of finding isomorphism classes of lattices over some orders,then we calculate the isomorphism classes of such lattices,thus give the value of|Sp₂（F_q）|when p∈{2,3,5}.