%0 Journal Article
%T On the period-index problem in light of the section conjecture
%A Jakob Stix
%J Mathematics
%D 2008
%I arXiv
%X Period and index of a curve $X/K$ over a $p$-adic local field $K$ such that the fundamental group $\pi_1(X/K)$ admits a splitting are shown to be powers of $p$. As a consequence, examples of curves over number fields are constructed where having sections is obstructed locally at a $p$-adic place. Hence the section conjecture holds for these curves as there are neither sections nor rational points.
%U http://arxiv.org/abs/0802.4125v1