| Résume | Grothendieck's section conjecture in anabelian geometry suggests to usesplittings of thefundamental group exact sequence to study rational points. Over number fields,splittings which locallycome from rational points are related to adelic points which survive all finitetorsor obstructions.We will discuss in the talk a refinement of Hoshi's counterexamples to a pro-$p$version of the section conjecture.In particular, we need to understand how badly the analogue of the sectionconjecture fails over finite fields. |
