On the Hasse principle for quartic hypersurfaces

TL;DR

This paper proves that smooth quartic hypersurfaces of dimension at least 28 over the rationals satisfy the Hasse principle, ensuring local-global solutions coincide for these high-dimensional cases.

Contribution

It establishes the Hasse principle for a broad class of high-dimensional quartic hypersurfaces over the rationals, extending previous results.

Findings

Hasse principle holds for quartic hypersurfaces of dimension ≥ 28

New techniques applied to high-dimensional algebraic varieties

Results contribute to understanding rational points on hypersurfaces

Abstract

We establish the Hasse principle for smooth projective quartic hypersurfaces of dimension greater than or equal to 28 defined over $\mathbb{Q}$.