Diophantine decidability for curves and Grothendieck's section conjecture

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 $X$.

This paper is withdrawn as the main result is already known