Diophantine decidability for curves and Grothendieck's section conjecture

2010/01/27 by Ambrus Pál, Ambrus Pal, Pal, Ambrus
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #math.NT #msc:11G30 #msc:11Y50 #msc:14G05

paper · pdf · doi:10.48550/arxiv.1001.4969

This paper is withdrawn as the main result is already known

arxiv created 2010/02/22 · arxiv updated 2010/02/26

Abstract

Let X be a smooth, projective, geometrically irreducible curve of genus at least two defined over a number field K. We prove that there is an algorithm that determines whether X has a K-rational point if Grothendieck's section conjecture holds for X.

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