We solve the question of the existence of a Poisson-Pinsker factor for
conservative ergodic infinite measure preserving action of a countable amenable
group by proving the following dichotomy: either it has totally positive
Poisson entropy (and is of zero type), or it possesses a Poisson-Pinsker
factor. If G is abelian and the entropy positive, the spectrum is absolutely
continuous (Lebesgue countable if G=\mathbb{Z}) on the whole L^{2}-space in the
first case and in the orthocomplement of the L^{2}-space of the Poisson-Pinsker
factor in the second.