Some Obstructions to Solvable Points on Higher Genus Curves

2022/11/18 by James Rawson, Rawson, James · 1 citation
Computer Science · Mathematics · #11G30 #11G35 #14G05 #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2211.10367

openalex publication_date 2022/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

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.

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• Solvable points on intersections of quadrics, cubics, and quartics

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