On the Section Conjecture over Function Fields and Finitely Generated Fields

  • Mohamed Saïdi

    University of Exeter, United Kingdom

Abstract

We investigate sections of the 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 if it holds over all number fields, under the condition of finiteness (of the -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.

Cite this article

Mohamed Saïdi, On the Section Conjecture over Function Fields and Finitely Generated Fields. Publ. Res. Inst. Math. Sci. 52 (2016), no. 3, pp. 335–357

DOI 10.4171/PRIMS/184