English

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}
}
R2 v1 2026-06-21T08:33:05.905Z