The field-of-norms functor and the Hilbert symbol for higher local fields

Details The field-of-norms functor and the Hilbert symbol for higher local fields The field-of-norms functor and the Hilbert symbol for higher local fields

2010-10-04

arxiv.org/abs/1010.0555v1

Mathematics

Number Theory

Scientific paper

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

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