Class Numbers and Algebraic Tori

2013/12/24 by Akinari Hoshi, Hoshi, Akinari, Ming-chang Kang +3
Computer Science · Mathematics · #11R33 #14E08 #20C10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Geometric and Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1312.6738

openalex publication_date 2013/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p be an odd prime number, D_p be the dihedral group of order 2p, h_p and h⁺_p be the class numbers of \bmQ(ζ_p) and \bmQ(ζ_p+ ζ_p^-1) respectively. Theorem. h_p⁺=1 if and only if, for any field k admitting a D_p-extension, all the algebraic D_p-tori over k are stably rational. A similar result for h_p=1 and C_p-tori is valid also.

Citations

• Algebraic tori - thirty years after

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