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.
Finite group subschemes of abelian varieties over finite fields
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abstract
Let $A$ be an abelian variety over a finite field $k$. The $k$-isogeny class of $A$ is uniquely determined by the Weil polynomial $f_A$. We assume that $f_A$ is separable. For a given prime number $\ell\neq\mathrm{char}\, k$ we give a classification of group schemes $B[\ell]$, where $B$ runs through the isogeny class, in terms of certain Newton polygons associated to $f_A$. As an application we classify zeta functions of Kummer surfaces over $k$.
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math.AG 1years
2024 1verdicts
UNVERDICTED 1representative citing papers
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Generalized Kummer surfaces over finite fields
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.