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

2022/11/21 by Jun-Hao Huang, Fan-Yun Hung, Huang, Jun-Hao +5
Computer Science · Mathematics · #Algebraic structures and combinatorial models #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2211.11249

openalex publication_date 2022/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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