Some arithmetic properties of Weil polynomials of the form t^2g+at^g+q^g

2020/01/04 by Alejandro J. Giangreco-Maidana, Giangreco-Maidana, Alejandro J.
Computer Science · Mathematics · #Coding theory and cryptography #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory

paper · doi:10.48550/arxiv.2001.01104

Abstract

An isogeny class A of abelian varieties defined over finite fields is said to be "cyclic" if every variety in A has a cyclic group of rational points. In this paper we study the local cyclicity of Weil-central isogeny classes of abelian varieties, i.e. those with Weil polynomials of the form f_A(t)=t^2g+at^g+q^g, as well as the local growth of the groups of rational points of the varieties in A after finite field extensions. We exploit the criterion: an isogeny class A with Weil polynomial f is cyclic if and only if f'(1) is coprime with f(1) divided by its radical.

Related

• Cyclic abelian varieties over finite fields in ordinary isogeny classes
• Weil polynomials of abelian varieties over finite fields with many rational points
• Weil polynomials of abelian varieties over finite fields
• Weil polynomials of small degree
• Isogeny Classes of Abelian Varieties over Finite Fields in the LMFDB