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The CARMENES instrument, mounted on the 3.5m telescope in Calar Alto Observatory (Spain), is a dual echelle spectrograph covering the wavelength ranges from 0.52 to 0.96 µm and from 0.96 to 1.71 µm, each of which performs high-accuracy long-term stable radial-velocity measurements. Since January 2016, it conducts a survey of more than 300 M dwarfs with the goal of detecting low-mass planets in their habitable zones. The TESS mission, monitoring the brightest and closer stars across the whole sky to discover transiting planets, is particularly designed to meet the same goal. The CARMENES survey is devoting a substantial number of nights to confirm and characterize transiting planet candidates around M dwarfs detected with TESS. Such planets, particularly those in the habitable zone of their host, comprise the most promising targets for atmospheric characterization with current and future ground- and space-based facilities. In this talk, I will review the most relevant results from the CARMENES-TESS synergy (e.g. GJ 357, TOI 442, TOI 732) and its efficiency and promptness to carry radial velocity follow-up. Besides the mass and orbital characterization of small planets around M dwarfs, this effort provides an essential step to understand the formation and composition of planets as a function of stellar host properties.

Precise characterisation of small planets around M dwarfs: the CARMENES-TESS follow-up program