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arxiv: 0903.0106 · v4 · submitted 2009-03-02 · 🧮 math.AG · math.NT

The groups of points on abelian varieties over finite fields

Sergey Rybakov This is my paper
classification 🧮 math.AG math.NT
keywords abelianclassfinitegroupspointsvarietiesalgebraclassification
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Let $A$ be an abelian variety with commutative endomorphism algebra over a finite field $k$. The $k$-isogeny class of $A$ is uniquely determined by a Weil polynomial $f_A$ without multiple roots. We give a classification of the groups of $k$-rational points on varieties from this class in terms of Newton polygons of $f_A(1-t)$.

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    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.