Some complements to the Lazard isomorphism

Annette Huber, Guido Kings, Niko Naumann
2010 Compositio Mathematica  
AbstractLazard showed in his seminal work (Groupes analytiquesp-adiques, Publ. Math. Inst. Hautes Études Sci. 26(1965), 389–603) that for rational coefficients, continuous group cohomology ofp-adic Lie groups is isomorphic to Lie algebra cohomology. We refine this result in two directions: first, we extend Lazard's isomorphism to integral coefficients under certain conditions; and second, we show that for algebraic groups over finite extensionsK/p, his isomorphism can be generalized toK-analytic cochains andK-Lie algebra cohomology.
doi:10.1112/s0010437x10004884 fatcat:5vdqzubk3veyvb4mc6eelxc2yy