The higher Hilbert pairing via (phi,G)-modules
Number Theory
2007-05-30 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0705.4269,
title = {The higher Hilbert pairing via (phi,G)-modules},
author = {Sarah Livia Zerbes},
journal= {arXiv preprint arXiv:0705.4269},
year = {2007}
}