Bloch-Kato exponential maps for local fields with imperfect residue fields

Details Bloch-Kato exponential maps for local fields with imperfect residue fields Bloch-Kato exponential maps for local fields with imperfect residue fields

2008-06-12

arxiv.org/abs/0806.2122v1

Mathematics

Number Theory

23 pages, generalisation of my previous results for higher dimensional local fields

Scientific paper

In this paper, we generalise the construction of the Bloch-Kato exponential map to complete discrete valuation fields of mixed characteristic (0,p) whose residue fields have a finite p-basis. As an application we prove an explicit reciprocity law, extending a result of Cherbonnier and Colmez in the classical case. This result relies on the calculation of the Galois cohomology of a p-adic representation V in terms of its (phi,G)-module.

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