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

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

2008-02-28

arxiv.org/abs/0802.4125v1

Mathematics

Algebraic Geometry

17 pages

Scientific paper

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.

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