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arXiv · 0802.4125

On the period-index problem in light of the section conjecture

Jakob Stix
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Abstract

Period and index of a curve $X/K$ over a $p$-adic local field $K$ such that the fundamental group $π_1(X/K)$ 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.

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Jakob Stix. 2008-02-28. On the period-index problem in light of the section conjecture. https://arxiv.org/abs/0802.4125

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