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arXiv · 0705.4269

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

Sarah Livia Zerbes
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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.

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Sarah Livia Zerbes. 2007-05-29. The higher Hilbert pairing via (phi,G)-modules. https://arxiv.org/abs/0705.4269

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