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arXiv · 2307.11440

Class numbers of multinorm-one tori

Fan-Yun Hung·Chia-Fu Yu
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Abstract

We present a formula for the class number of a multinorm one torus $T_{L/k}$ associated to any \'etale 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.

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Fan-Yun Hung, Chia-Fu Yu. 2023-07-21. Class numbers of multinorm-one tori. https://arxiv.org/abs/2307.11440

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