Work

Some Obstructions to Solvable Points on Higher Genus Curves

Year: 2025

Type: article

Abstract: It is known that for a curve defined over ℚ of genus g ≤ 4 , there exists a point on the curve defined over a solvable extension of ℚ . We relate points on curves of genus g ≥ 5 over solvable extensions to the Bombieri–Lang conjecture. Specifically, we show that varieties parametrising points defined over extensions with a fixed solvable Galois group are of general type. Moreover, we show the existence of certain subvarieties in these varieties imply the existence of solvable morphisms from the curve.

Source: Journal de Théorie des Nombres de Bordeaux

DOI: 10.5802/jtnb.1304

Author: James Rawson

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Engineering and Physical Sciences Research Council

Award: Maths DTP 2021-22 University of Warwick

OpenAlex ID: W4409004506

FWCI: 1.756

Cites: 10

Cited by: 1

Related to: 10