Quadratic points on intersections of two quadrics

TL;DR

This paper proves that smooth intersections of two quadrics of dimension at least 2 over a number field always have a rational zero-cycle of degree 2, revealing a key property about their rational points.

Contribution

It establishes that such intersections have an index dividing 2, providing new insight into their rational zero-cycles over number fields.

Findings

Index divides 2 for these intersections.

Existence of rational zero-cycle of degree 2.

Advances understanding of rational points on intersections of quadrics.

Abstract

We prove that a smooth complete intersection of two quadrics of dimension at least $2$ over a number field has index dividing $2$, i.e., that it possesses a rational $0$-cycle of degree $2$.