The higher Hilbert pairing via (phi,G)-modules

Details The higher Hilbert pairing via (phi,G)-modules The higher Hilbert pairing via (phi,G)-modules

2007-05-29

arxiv.org/abs/0705.4269v1

Mathematics

Number Theory

23 pages

Scientific paper

We prove the Tate duality for higher dimensional local fields of mixed characteristic (0,p), when p is an odd prime, using the theory of higher fields of norms. Assuming that p is not ramified in the basefield, we then use this construction to define the higher Hilbert pairing. In particular, we show that the Hilbert pairing is non-degenerate, and we re-discover the formulae of Brueckner and Vostokov.

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