On classification of groups of points on abelian varieties over finite\n fields

2014/01/08 by Sergey Rybakov, Rybakov, Sergey
Computer Science · Mathematics · #Coding theory and cryptography #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1401.1652

Abstract

In this paper we improve our previous results on classification of groups of\npoints on abelian varieties over finite fields. The classification is given in\nterms of the Weil polynomial of abelian varieties in a given k-isogeny class.\n

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• The groups of points on abelian surfaces over finite fields
• Weil polynomials of abelian varieties over finite fields with many rational points
• Finite group subschemes of abelian varieties over finite fields
• Cyclic abelian varieties over finite fields in ordinary isogeny classes
• Weil polynomials of abelian varieties over finite fields