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Lazard showed in his seminal work "Groupes analytiques $p$-adiques" that forrational coefficients continuous group cohomology of $p$-adic Lie-groups isisomorphic to Lie-algebra cohomology. We refine this result in two directions:firstly we extend his isomorphism under certain conditions to integralcoefficients and secondly, we show that for algebraic groups, his isomorphismcan be realized by differentiating locally analytic cochains.

Some complements to the Lazard isomorphism