Lazard同构的一些补
Some complements to the Lazard isomorphism
摘要：
拉扎德表明，在他的开创性工作“Groupes analytiques $p$ -adiques”，为合理的系数连续群上同调的$p$ -进李群是同构的李代数上同调。我们在两个方向改进了这个结果：首先，我们在一定条件下将他的同构推广到整系数，其次，我们证明了对于代数群，他的同构可以通过局部解析上链的微分来实现。
英文摘要：
Lazard showed in his seminal work "Groupes analytiques $p$-adiques" that for rational coefficients continuous group cohomology of $p$-adic Lie-groups is isomorphic to Lie-algebra cohomology. We refine this result in two directions: firstly we extend his isomorphism under certain conditions to integral coefficients and secondly, we show that for algebraic groups, his isomorphism can be realized by differentiating locally analytic cochains.
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