Finite group subschemes of abelian varieties over finite fields

2010/06/30 by Rybakov, Sergey
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1006.5959

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 ℓ\neqchar k we give a classification of group schemes B[ℓ], 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.

Related

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• On classification of groups of points on abelian varieties over finite\n fields
• Weil polynomials of abelian varieties over finite fields with many rational points
• Weil polynomials of abelian varieties over finite fields
• Isogeny graphs of ordinary abelian varieties