Norm one tori and Hasse norm principle, II: Degree 12 case
نویسندگان
چکیده
Let k be a field, T an algebraic k-torus, X smooth k-compactification of and PicX‾ the Picard group X‾=X×kk‾. Hoshi, Kanai Yamasaki [HKY22] determined H1(k,PicX‾) for norm one tori T=RK/k(1)(Gm) gave necessary sufficient condition Hasse principle extensions K/k number fields with [K:k]=n≤15 n≠12. In this paper, we determine 64 cases H1(k,PicX‾)≠0 give [K:k]=12.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2023
ISSN: ['0022-314X', '1096-1658']
DOI: https://doi.org/10.1016/j.jnt.2022.09.006