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arXiv · 2211.11249

Computing Tate-Shafarevich groups of multinorm one tori of Kummer type

Jun-Hao Huang·Fan-Yun Hung·Pei-Xin Liang·Chia-Fu Yu
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Abstract

A multinorm one torus associated to a commutative étale algebra $L$ over a global field $k$ is of Kummer type if each factor of $L$ is a cyclic Kummer extension. In this paper we compute the Tate-Shafarevich group of such tori based on recent works of Bayer-Fluckiger, T.-Y. Lee and Parimala, and of T.-Y.~Lee. We also implement an effective algorithm using SAGE which computes the Tate-Shafarevich groups when each factor of $L$ is contained in a fixed concrete bicyclic extension of $k$.

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Jun-Hao Huang, Fan-Yun Hung, Pei-Xin Liang, Chia-Fu Yu. 2022-11-21. Computing Tate-Shafarevich groups of multinorm one tori of Kummer type. https://arxiv.org/abs/2211.11249

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