On p-adic density of rational points on K3 surfaces

TL;DR

This paper proves that infinitely many K3 surfaces over Q have rational points dense in their p-adic points for all primes p, with some surfaces dense for primes p ≡ 3 mod 4 and p > 7.

Contribution

It establishes the existence of infinitely many K3 surfaces with dense rational points in p-adic topology for all primes p and identifies specific conditions for density across primes.

Findings

Existence of infinitely many K3 surfaces with dense rational points in p-adic topology for all primes p.

Existence of a K3 surface dense in p-adic points for primes p ≡ 3 mod 4 and p > 7.

Demonstrates p-adic density properties of rational points on K3 surfaces.

Abstract

We show that, for every prime number p, there exist infinitely many K3 surfaces over Q whose rational points lie dense in the space of p-adic points. We also show that there exists a K3 surface over Q whose rational points lie dense in the space of p-adic points for all prime numbers p with p congruent to 3 mod 4 and greater than 7.