Abstract
Let C be an algebraically closed, nonarchimedean field of mixed characteristic which is complete under a rank one valuation; let O ⊆ C be its ring of integers, with maximal ideal m and residue field k. The reader may assume that C is the completion of an algebraic closure of Qp. The main aim of this note is to outline a proof of the following result, which was first announced by the third author during his series of Fall 2014 lectures at the MSRI. Details, generalisations, and further results will be presented in a forthcoming article. In particular, this will include a “comparison isomorphism”-style result.
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