The norm residue symbol for higher local fields

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The norm residue symbol for higher local fields

Flórez, Jorge

Journal of number theory, June 2022, 2022-06-00, Volume: 235

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In this paper we investigate the Kummer pairing associated to an arbitrary (one-dimensional) formal group. In particular, we obtain formulae describing the values of the pairing in terms of multidimensional p-adic differentiation, the logarithm of the formal group, the generalized trace and the norm on Milnor K-groups. The results are a generalization to higher-dimensional local fields of Kolyvagin's explicit reciprocity laws. In particular, they constitute a generalization of the reciprocity laws of Artin-Hasse, Iwasawa and Wiles.

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Flórez, Jorge

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