Khan, S.Miglio, AWillett, E.Mosser, BenoitElsworth, YAnderson, R. I.Girardi, LBelkacem, K.Brown, A. G. A.Cantat-Gaudin, T.Casagrande, Luca2025-03-022025-03-020004-6361https://hdl.handle.net/1885/733736587Gaia EDR3 has provided unprecedented data that has generated a great deal of interest in the astrophysical community, even though systematics affect the reported parallaxes at the level of ∼10 μas. Independent distance measurements are available from asteroseismology of red-giant stars with measurable parallaxes, whose magnitude and colour ranges more closely reflect those of other stars of interest. In this paper we determine distances to nearly 12 500 red-giant-branch and red clump stars observed by Kepler, K2, and TESS. This was done via a grid-based modelling method, where global asteroseismic observables, and constraints on the photospheric chemical composition and on the unreddened photometry are used as observational inputs. This large catalogue of asteroseismic distances allows us to provide a first comparison with Gaia EDR3 parallaxes. Offset values estimated with asteroseismology show no clear trend with ecliptic latitude or magnitude, and the trend whereby they increase (in absolute terms) as we move towards redder colours is dominated by the brightest stars. The correction model proposed by Lindegren et al. (2021a) is not suitable for all the fields considered in this study. We find a good agreement between asteroseismic results and model predictions of the red clump magnitude. We discuss possible trends with the Gaia scan law statistics, and show that two magnitude regimes exist where either asteroseismology or Gaia provides the best precision in parallax.Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. R.I.A. and S.K. are funded by the Swiss National Science Foundation (SNSF) through an Eccellenza Professorial Fellowship (award PCEFP2_194638). A.M. and E.W. acknowledge support from the ERC Consolidator Grant funding scheme (project ASTEROCHRONOMETRY, G.A. n. 772293). This research was supported by the International Space Science Institute (ISSI) in Bern, through ISSI International Team project #490, SHoT: The Stellar Path to the Ho Tension in the Gaia, TESS, LSST and JWST Era. We also wish to thank the referee who provided a very positive report.application/pdfen-AU©2023 The authorshttp://creativecommons.org/licenses/by/4.0/asteroseismologyastrometryparallaxesstars: distancesstars: low-massstars: oscillations202310.1051/0004-6361/2023461962023-12-24Creative Commons Attribution licence