Функтор поле норм и символ Гильберта для многомерных локальных полей

This is a joint paper with R. Jenny. The field-of-norms functor is applied to deduce explicit reciprocity formulae for the Hilbert symbol in the mixed characteristic case from the explicit formula for the Witt symbol in characteristic $p>2$ in the context of higher local fields. Is is shown that a “very special case” of this construction gives Vostokov's explicit formula.