The nearest stars provide a fundamental constraint for our understanding of stellar physics and the Galaxy. The nearby sample serves as an anchor where all objects can be seen and understood with precise data. This work is triggered by the most recent data release of the astrometric space mission Gaia and uses its unprecedented high precision parallax measurements to review the census of objects within 10 pc. The first aim of this work was to compile all stars and brown dwarfs within 10 pc observable by Gaia, and compare it with the Gaia Catalogue of Nearby Stars as a quality assurance test. We complement the list to get a full 10 pc census, including bright stars, brown dwarfs, and exoplanets. We started our compilation from a query on all objects with a parallax larger than 100 mas using SIMBAD. We completed the census by adding companions, brown dwarfs with recent parallax measurements not in SIMBAD yet, and vetted exoplanets. The compilation combines astrometry and photometry from the recent Gaia Early Data Release 3 with literature magnitudes, spectral types and line-of-sight velocities. We give a description of the astrophysical content of the 10 pc sample. We find a multiplicity frequency of around 28%. Among the stars and brown dwarfs, we estimate that around 61% are M stars and more than half of the M stars are within the range M3.0 V to M5.0 V. We give an overview of the brown dwarfs and exoplanets that should be detected in the next Gaia data releases along with future developments. We provide a catalogue of 540 stars, brown dwarfs, and exoplanets in 339 systems, within 10 pc from the Sun. This list is as volume-complete as possible from current knowledge and provides benchmark stars that can be used, for instance, to define calibration samples and to test the quality of the forthcoming Gaia releases. It also has a strong outreach potential.
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