International audienceThe ultracool dwarf star TRAPPIST-1 hosts seven Earth-size transiting planets, some of which could harbor liquid water on their surfaces. Ultraviolet observations are essential to measuring their high-energy irradiation and searching for photodissociated water escaping from their putative atmospheres. Our new observations of the TRAPPIST-1 Lyα line during the transit of TRAPPIST-1c show an evolution of the star emission over three months, preventing us from assessing the presence of an extended hydrogen exosphere. Based on the current knowledge of the stellar irradiation, we investigated the likely history of water loss in the system. Planets b to d might still be in a runaway phase, and planets within the orbit of TRA...