Local solubility for a family of quadrics over a split quadric surface

TL;DR

This paper investigates the density of rational points on certain diagonal quadric surfaces that are locally soluble, focusing on those lying on a split quadric surface, contributing to understanding their distribution.

Contribution

It introduces a new analysis of local solubility for a family of quadrics over split surfaces, advancing the understanding of rational points on these varieties.

Findings

Identifies conditions for local solubility of the quadrics.

Provides density estimates for rational points on these surfaces.

Enhances understanding of the distribution of solutions.

Abstract

We study the density of everywhere locally soluble diagonal quadric surfaces, parameterised by rational points that lie on a split quadric surface.