DOCUMENTA MATHEMATICA, Vol. 21 (2016), 1607-1643

Jiangwei Xue,Tse-Chung Yang, and Chia-Fu Yu

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 $q=pa$ 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.

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