Rational points on intersections of cubic and quadric hypersurfaces

TL;DR

This paper studies the Hasse principle for intersections of quadric and cubic hypersurfaces over the rational numbers, aiming to understand when such intersections have rational points.

Contribution

It provides new insights into the validity of the Hasse principle for specific algebraic varieties defined by quadric and cubic equations.

Findings

Conditions under which the Hasse principle holds for these intersections

Counterexamples where the Hasse principle fails

Criteria for the existence of rational points

Abstract

We investigate the Hasse principle for complete intersections cut out by a quadric and cubic hypersurface defined over the rational numbers.