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arXiv · 1807.09909

The Hasse principle for finite Galois modules allowing exceptional sets of positive density

Yasuhiro Ishitsuka·Tetsushi Ito
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Abstract

We study a variant of the Hasse principle for finite Galois modules, allowing exceptional sets of positive density. For a Galois module whose underlying abelian group is isomorphic to $\mathbb{F}_p^{\oplus r}$ ($r \leq 2$), we show that the product of the restriction maps for places in a set of places $S$ is injective if the Dirichlet density of $S$ is strictly larger than $1 - p^{-r}$. We give applications to the local-global divisibility problem for elliptic curves and the Hasse principle for flexes on plane cubic curves.

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Yasuhiro Ishitsuka, Tetsushi Ito. 2018-07-26. The Hasse principle for finite Galois modules allowing exceptional sets of positive density. https://arxiv.org/abs/1807.09909

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