Rational Points on the Intersection of Three Quadrics

TL;DR

This paper proves the Hasse principle and weak approximation for smooth intersections of three quadrics in at least 19 variables over any number field, advancing understanding of rational points on such varieties.

Contribution

It establishes the Hasse principle and weak approximation for these intersections over arbitrary number fields, extending previous results to a broader class of varieties.

Findings

Proves the Hasse principle for intersections of three quadrics in ≥19 variables.

Establishes weak approximation for these varieties over any number field.

Extends known results to more general settings.

Abstract

This paper proves the Hasse principle and weak approximation for varieties defined by the smooth intersection of three quadratics in at least 19 variables, over arbitrary number fields.