2-adic point counting on K3 surfaces

2022/02/22 by Andreas-Stephan Elsenhans, Elsenhans, Andreas-Stephan, Jörg Jahnel +1
Mathematics · #11G25 #14F20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Primary 14J28 #Secondary 20G25 #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2202.10853

openalex publication_date 2022/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article reports on an approach to point counting on algebraic varieties over finite fields that is based on a detailed investigation of the 2-adic orthogonal group. Combining the new approach with a p-adic method, we count the number of points on some K3 surfaces over the field \bbF _p, for all primes p < 10⁸.

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