We prove that every amenable group of cohomological dimension two whose integral ring is a domain solvable and investigate certain homological finiteness properties groups satisfy the analytic zero divisor conjecture act on an acyclic CW-complex with stabilisers.

Abstract We study the Hodge filtration on local cohomology sheaves of a smooth complex algebraic variety along closed subscheme Z in terms log resolutions and derive applications regarding cohomological dimension, Du Bois complex, vanishing reflexive differentials associated to .