  The maximum number density of Active Galactic Nuclei (AGNs), as deduced from
X-ray studies, occurs at z<~1, with lower luminosity objects peaking at smaller
redshifts. Optical studies lead to a different evolutionary behaviour, with a
number density peaking at z~2 independently of the intrinsic luminosity, but
this result is limited to active nuclei brighter than the host galaxy. A
selection based on optical variability can detect low luminosity AGNs (LLAGNs),
where the host galaxy light prevents the identification by non-stellar colours.
We want to collect X-ray data in a field where it exists an optically-selected
sample of "variable galaxies'', i.e. variable objects with diffuse appearance,
to investigate the X-ray and optical properties of the population of AGNs,
particularly of low luminosity ones, where the host galaxy is visible. We
observed a field of 0.2 deg^2 in the Selected Area 57, for 67ks with
XMM-Newton. We detected X-ray sources, and we correlated the list with a
photographic survey of SA 57, complete to B_J~23 and with available
spectroscopic data. We obtained a catalogue of 140 X-ray sources to limiting
fluxes 5x10^-16, 2x10^-15 erg/cm^2/s in the 0.5-2 keV and 2-10 keV
respectively, 98 of which are identified in the optical bands. The X-ray
detection of part of the variability-selected candidates confirms their AGN
nature. Diffuse variable objects populate the low luminosity side of the
sample. Only 25/44 optically-selected QSOs are detected in X-rays. 15% of all
QSOs in the field have X/O<0.1.
