Abstract
For a field F, let G n (F) = {{a,Φ n (a)} ∈ K 2(F) | a,Φ n (a) ∈ F*}, where Φ n (x) is the n-th cyclotomic polynomial. At first, by using Faltings’ theorem on Mordell conjecture it is proved that if F is a number field and if n ≠ 4, 8, 12 is a positive integer having a square factor then G n (F) is not a subgroup of K 2(F), and then by using the results of Manin, Grauert, Samuel and Li on Mordell conjecture theorem for function fields, a similar result is established for function fields over an algebraically closed field.
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This work was supported by the National Natural Science Foundation of China (Grant No. 10371061)
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Xu, K., Liu, M. On the torsion in K 2 of a field. Sci. China Ser. A-Math. 51, 1187–1195 (2008). https://doi.org/10.1007/s11425-008-0071-6
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DOI: https://doi.org/10.1007/s11425-008-0071-6