  We used the OSIRIS camera at the 10.4 m Gran Telescopio Canarias (GTC) to
monitor the astrometric motion of the L4.5 dwarf 2M1821$+$14 over 17 months.
The astrometric residuals of eleven epochs have a r.m.s. dispersion of 0.4 mas,
which is larger than the average precision of 0.23 mas per epoch and hints
towards an additional signal or excess noise. Comparison of the
point-spread-functions in OSIRIS and FORS2/VLT images reveals no differences
critical for high-precision astrometry, despite the GTC's segmented primary
mirror. We attribute the excess noise to an unknown effect that may be
uncovered with additional data. For 2M1821$+$14, we measured a relative
parallax of $106.15 \pm 0.18$ mas and determined a correction of $0.50\pm0.05$
mas to absolute parallax, leading to a distance of $9.38 \pm0.03$ pc. We
excluded at 3-$\sigma$ confidence the presence of a companion to 2M1821$+$14
down to a mass ratio of 0.1 ($\approx 5\, M_\mathrm{Jupiter}$) with a period of
50--1000 days and a separation of 0.1--0.7 au. The accurate parallax allowed us
to estimate the age and mass of 2M1821$+$14 of 120--700 Myr and
0.049$^{+0.014}_{-0.024}$ M$_\odot$, thus confirming its intermediate age and
substellar mass. We complement our study with a parallax and proper motion
catalogue of 587 stars ($i'\simeq15.5-22$) close to 2M1821$+$14, used as
astrometric references. This study demonstrates sub-mas astrometry with the
GTC, a capability applicable for a variety of science cases including the
search for extrasolar planets and relevant for future astrometric observations
with E-ELT and TMT.
