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

Abstract

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.

arXiv comment23 pages, generalisation of my previous results for higher dimensional local fields

Cited by in corpus (1)

• Multivariable $(\phi ,\Gamma )$-modules and Representations of Products of Galois Groups: The Case of Imperfect Residue Field