  Gamma-ray bursts are the most energetic known explosions. Despite fading
rapidly, they allow to measure redshift and important properties of their
host-galaxies. We report the photometric and spectroscopic study of GRB 160203A
and its host-galaxy. Fine-structure absorption lines, detected in the afterglow
at different epochs, allow us to investigate variability due to the strong
fading background source. We obtained two optical to near-infrared spectra of
the afterglow with X-shooter on ESO/VLT, 18 min and 5.7 hrs after the burst,
allowing us to investigate temporal changes of fine-structure absorption lines.
We measured HI column density log N(HI/cm-2)=21.75+/-0.10, and several
heavy-element ions along the GRB sight-line in the host-galaxy:
SiII,AlII,AlIII,CII,NiII,SiIV,CIV,ZnII,FeII, and FeII and SiII fine structure
transitions from energetic levels excited by the afterglow, at a redshift
z=3.518. We measured [M/H]TOT=-0.78+/-0.13 and [Zn/Fe]FIT=0.69+/-0.15,
representing the total(dust-corrected) metallicity and dust depletion,
respectively. We detected additional intervening systems along the line of
sight at z=1.03,z=1.26,z=1.98,z=1.99,z=2.20 and z=2.83. We could not measure
significant variability in the fine-structure lines throughout all the
observations and determined an upper limit for the GRB distance from the
absorber of d<300 pc, adopting the canonical UV pumping scenario. However, we
note that the quality of our data is not sufficient to conclusively rule out
collisions as an alternative mechanism. GRB 160203A belongs to a growing sample
of GRBs with medium resolution spectroscopy, provided by the Swift/X-shooter
legacy program, which enables detailed investigation of the interstellar medium
in high-redshift GRB host-galaxies. In particular, this host galaxy shows
relatively high metal enrichment and dust depletion already in place when the
universe was only 1.8 Gyr old.
