Some complements to the Lazard isomorphism

Abstract

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.

Final version, to appear in Compositio Mathematica

References in corpus (1)

• Algebras of p-adic distributions and admissible representations

Cited by in corpus (3)

• The Algebraic Duality Resolution at $p=2$
• Locally analytic representations and sheaves on the Bruhat-Tits building
• On an analytic version of Lazard's isomorphism