Infinitely many supersingular primes for some Mumford's abelian fourfolds

2025/11/10 by Fangu Chen, Chen, Fangu · 1 citation
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2511.06654

openalex publication_date 2025/11/10 · openalex created_date 2025/11/12 · openalex updated_date 2026/07/28

Abstract

Elkies proved the infinitude of supersingular primes for elliptic curves over real number fields. We generalize Elkies' result to some abelian fourfolds in Mumford's families, and more generally, to certain families of Kuga-Satake abelian varieties. The proof relies on the study of local deformation spaces at closed points of the integral model of a Hodge-type Shimura variety, based on the work of Madapusi, and on the analysis of real points of a Shimura curve, based on the work of Shimura.

Citations

• Infinitely many primes of basic reduction for some abelian fourfolds
• On distribution of supersingular primes of abelian varieties and K3 surfaces
• Unlikely Intersections in Finite Characteristic
• The Tate conjecture for K3 surfaces in odd characteristic
• Integral canonical models for Spin Shimura varieties
• Real multiplication on K3 surfaces and Kuga Satake varieties

Cited by

• Superspecial primes for QM abelian surfaces over real number fields

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