2023/07/21 by Fan-Yun Hung, Hung, Fan-Yun, Chia‐Fu Yu +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2307.11440
openalex publication_date 2023/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a formula for the class number of a multinorm one torus TL/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.