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The groups of points on abelian surfaces over finite fields

· 2010 · math.AG · arXiv 1007.0115

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abstract

Let $A$ be an abelian surface over a finite field $k$. The $k$-isogeny class of $A$ is uniquely determined by a Weil polynomial $f_A$ of degree 4. We give a classification of the groups of $k$-rational points on varieties from this class in terms of $f_A$.

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Generalized Kummer surfaces over finite fields

math.AG · 2024-04-01 · unverdicted · novelty 5.0

Refines Katsura theorem on abelian surface quotients birational to K3 surfaces and computes Frobenius traces on NS groups of supersingular generalized Kummer surfaces over finite fields.

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  • Generalized Kummer surfaces over finite fields math.AG · 2024-04-01 · unverdicted · none · ref 27 · internal anchor

    Refines Katsura theorem on abelian surface quotients birational to K3 surfaces and computes Frobenius traces on NS groups of supersingular generalized Kummer surfaces over finite fields.