On distribution of supersingular primes of abelian varieties and K3 surfaces

2025/04/10 by Hui, Chun-Yin · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2504.08088

Abstract

Let X be an abelian variety or a K3 surface defined over a number field K. We prove that the density of the supersingular primes of X is zero if X is non-CM. By applying an effective Chebotarev density theorem of Serre, we obtain asymptotic upper bounds of the counting function for these supersingular primes.

Cited by

• Infinitely many supersingular primes for some Mumford's abelian fourfolds
• Positive density of primes of ordinary reduction for abelian varieties of simple signature

Related

• Distribution of supersingular primes for abelian surfaces
• Ordinary Primes for Abelian Surfaces
• Positive density of primes of ordinary reduction for abelian varieties of simple signature
• On counting certain abelian varieties over finite fields
• Infinitely many supersingular primes for some Mumford's abelian fourfolds