Norm one tori and Hasse norm principle, II: Degree 12 case

2020/03/18 by Hoshi, Akinari, Kanai, Kazuki, Yamasaki, Aiichi · 1 citation
#11E72 #12F20 #13A50 #14E08 #20C10 #20G15 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2003.08253

Abstract

Let k be a field, T be an algebraic k-torus, X be a smooth k-compactification of T and \rm Pic X be the Picard group of X=X×_kk. Hoshi, Kanai and Yamasaki [HKY22] determined H¹(k,\rm Pic X) for norm one tori T=R⁽¹⁾_K/k(G_m) and gave a necessary and sufficient condition for the Hasse norm principle for extensions K/k of number fields with [K:k]=n≤ 15 and n≠ 12. In this paper, we determine 64 cases with H¹(k,\rm Pic X)≠ 0 and give a necessary and sufficient condition for the Hasse norm principle for K/k where [K:k]=12.

Cited by

• Hasse norm principle for extensions of prime squared degree

Related

• Norm one tori and Hasse norm principle, III: Degree 16 case
• Norm one tori and Hasse norm principle
• Hasse norm principle for M₁₁ and J₁ extensions
• Hasse norm principle for Heisenberg extensions of degree p³
• Explicit methods for the Hasse norm principle and applications to A_n and S_n extensions