On Superspecial Abelian Surfaces over Finite Fields

In this paper we establish a new lattice description for superspecial abelian varieties over a finite field $\Fq$ of $q=p^a$ elements. Our description depends on the parity of the exponent $a$ of $q$. When $q$ is an odd power of the prime $p$, we give an explicit formula for the number of superspecial abelian surfaces over $\Fq$.

2010 Mathematics Subject Classification: 11R52, 11G10

Keywords and Phrases: supersingular abelian surfaces, class number formula, Galois cohomology.

Full text: dvi.gz 91 k, dvi 306 k, ps.gz 440 k, pdf 455 k.

Home Page of DOCUMENTA MATHEMATICA