Transporting cohomology in Lazard correspondence

摘要

Lazard correspondence provides an isomorphism of categories between finitely generated nilpotent pro-p groups of nilpotency class smaller than p and finitely generated nilpotent Z(p)-Lie algebras of nilpotency class smaller than p. Denote by H-Gr(i) and H-Lie(i) the group cohomology functors and the Lie cohomology functors respectively. The aim of this paper is to show that for i = 0, 1 and 2, and for a given category of modules the cohomology functors H-Gr(i) oexp and H-Lie(i) are naturally equivalent. A similar result is proved for i = 3 with the relative cohomology groups.