Pairs of quadrics in 11 variables

TL;DR

This paper establishes an asymptotic formula for counting rational points within expanding regions on non-singular intersections of pairs of quadrics in at least 11 variables.

Contribution

It provides the first asymptotic count for rational points on such intersections in high-dimensional spaces, extending previous results.

Findings

Asymptotic formula for rational points in high dimensions

Applicable to non-singular intersections of pairs of quadrics

Advances understanding of rational points in algebraic geometry

Abstract

For non-singular intersections of pairs of quadrics in 11 or more variables, we prove an asymptotic for the number of rational points in an expanding box.