Diophantine decidability for curves and Grothendieck's section conjecture

Ambrus Pal

Diophantine decidability for curves and Grothendieck's section conjecture

Number Theory 2010-02-22 v2

Authors: Ambrus Pal

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 $X$ .

Keywords

diophantine decidability curves Grothendieck's section conjecture rational points algorithm

Cite

@article{arxiv.1001.4969,
  title  = {Diophantine decidability for curves and Grothendieck's section conjecture},
  author = {Ambrus Pal},
  journal= {arXiv preprint arXiv:1001.4969},
  year   = {2010}
}

Comments

This paper is withdrawn as the main result is already known

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