Class Numbers and Algebraic Tori
Hoshi, Akinari · Kang, Ming-chang · Yamasaki, Aiichi
Original · EN
Let p be an odd prime number, Dₚ be the dihedral group of order 2p, hₚ and h+ₚ be the class numbers of Q(ζₚ) and Q(ζₚ+ ζₚ⁻¹) respectively. Theorem. hₚ+=1 if and only if, for any field k admitting a Dₚ-extension, all the algebraic Dₚ-tori over k are stably rational. A similar result for hₚ=1 and Cₚ-tori is valid also.
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