  We have obtained deep far- (FUV) and near-ultraviolet (NUV) images of the
inner region of the dense globular cluster M15 with the Advanced Camera for
Surveys on board the Hubble Space Telescope. The FUV-NUV colour-magnitude
diagram shows a well defined track of horizontal branch stars, as well as a
trail of blue stragglers and white dwarfs. The main sequence turn-off is
clearly visible at FUV~23.5 mag and FUV-NUV~3 mag, and the main sequence stars
form a prominent track that extends at least two magnitudes below the main
sequence turn-off. As such, this is the deepest FUV-NUV colour-magnitude
diagram of a globular cluster presented so far. Cataclysmic variable and blue
straggler candidates are the most centrally concentrated stellar populations,
which might either be an effect of mass segregation or reflect the preferred
birthplace in the dense cluster core of such dynamically-formed objects. We
find 41 FUV sources that exhibit significant variability. We classify the
variables based on an analysis of their UV colours and variability properties.
We find four previously known RR Lyrae and 13 further RR Lyrae candidates, one
known Cepheid and six further candidates, six cataclysmic variables, one known
and one probable SX Phoenicis star, and the well known low-mass X-ray binary
AC211. Our analysis represents the first detection of SX Phoenicis pulsations
in the FUV. We find that Cepheids, RR Lyraes and SX Phoenicis exhibit massive
variability amplitudes in this waveband (several mags).
