  We study the infrared behaviour of the pure Yang-Mills correlators using
relations that are well defined in the non-perturbative domain. These are the
Slavnov-Taylor identity for three-gluon vertex and the Schwinger-Dyson equation
for ghost propagator in the Landau gauge. We also use several inputs from
lattice simulations. We show that lattice data are in serious conflict with a
widely spread analytical relation between the gluon and ghost infrared critical
exponents. We conjecture that this is explained by a singular behaviour of the
ghost-ghost-gluon vertex function in the infrared. We show that, anyhow, this
discrepancy is not due to some lattice artefact since lattice Green functions
satisfy the ghost propagator Schwinger-Dyson equation. We also report on a
puzzle concerning the infrared gluon propagator: lattice data seem to favor a
constant non vanishing zero momentum gluon propagator, while the Slavnov-Taylor
identity (complemented with some regularity hypothesis of scalar functions)
implies that it should diverge.
