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arXiv · 1512.01207

On the section conjecture over function fields and finitely generated fields

Mohamed Saidi
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Abstract

We investigate sections of arithmetic fundamental groups of hyperbolic curves over function fields. As a consequence we prove that the anabelian section conjecture of Grothendieck holds over all finitely generated fields over $\Bbb Q$ if it holds over all number fields, under the condition of finiteness (of the $\ell$-primary parts) of certain Shafarevich-Tate groups. We also prove that if the section conjecture holds over all number fields then it holds over all finitely generated fields for curves which are defined over a number field.

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Mohamed Saidi. 2015-12-03. On the section conjecture over function fields and finitely generated fields. https://arxiv.org/abs/1512.01207

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