Diophantine decidability for curves and Grothendieck's section conjecture

Details Diophantine decidability for curves and Grothendieck's section conjecture Diophantine decidability for curves and Grothendieck's section conjecture

2010-01-27

arxiv.org/abs/1001.4969v2

Mathematics

Number Theory

This paper is withdrawn as the main result is already known

Scientific paper

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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