Abstract
Let K be a field of characteristic 0 complete with respect to a non-trivial discrete valuation with perfect residue field k of characteristic p>0. Let V be a p-adic representation of the absolute Galois group of K. We compute explicitly Kato's filtration on the continuous cohomology group H1(K,V). When k is finite, we give a simple proof of Hyodo's celebrated result Hg1(K,V)=Hst1(K,V) when V is a potentially semi-stable Galois representation.
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