Finite group subschemes of abelian varieties over finite fields

Details Finite group subschemes of abelian varieties over finite fields Finite group subschemes of abelian varieties over finite fields

2010-06-30

arxiv.org/abs/1006.5959v1

Mathematics

Algebraic Geometry

14 pages

Scientific paper

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 $f_A$ has no multiple roots. For a given prime number $\ell\neq\ch k$ we give a classification of groupschemes $B[\ell]$, 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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