Solvable points on smooth projective varieties

TL;DR

This paper proves that smooth projective varieties of small degree over fields algebraic over Q have rational points over some solvable field extension, expanding understanding of rational points in algebraic geometry.

Contribution

It demonstrates the existence of rational points on small degree varieties over solvable extensions, a new result in the study of rational points over algebraic fields.

Findings

Small degree varieties have rational points over solvable extensions

Existence of points depends on the field being algebraic over Q

Provides conditions for points on smooth projective varieties

Abstract

We establish that smooth, geometrically integral projective varieties of small degree are not pointless in suitable solvable extensions of their field of definition, provided that this field is algebraic over $\Bbb Q$.