arXiv subjects

Fan-Yun Hung

Publications and source records attributed to Fan-Yun Hung.

2 recordsLinked to original sources

arXiv2023

Class numbers of multinorm-one tori

We present a formula for the class number of a multinorm one torus $T_{L/k}$ associated to any étale algebra $L$ over a global field $k$. This is deduced from a formula for analogues of invariants introduced by T.~Ono, which are interpreted as a generalization of Gauss genus theory. This paper includes the variants of Ono's invariant for arbitrary $S$-ideal class numbers and the narrow version, generalizing results of Katayama, Morishita, Sasaki and Ono.

math.NT↗

arXiv2022

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

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 $k$.

math.NT↗