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Chronology of our Galaxy from Gaia colour-magnitude diagram fitting (ChronoGal) -- III. Age and metallicity distribution of Gaia-Sausage-Enceladus stars near the Sun

Context. Gaia-Sausage-Enceladus is considered the last major merger that contributed to the formation of the Milky Way. Its remnants dominate the nearby accreted stellar halo of the Milky Way. Aim. We aim to characterise the star formation history of Gaia-Sausage-Enceladus through the age and metallicity of its stellar populations. Methods. From Gaia DR3 data, we dynamically define three Gaia-Sausage-Enceladus samples with different criteria and possible degrees of contamination from other substructures in the halo. Then, we derive the stellar age and metallicity distributions using the CMDfit.Gaia package. Results. We identify three main populations of stars and a fourth smaller one following an almost linear age-[M/H] relation. The three oldest populations correspond to the bulk of the star formation that lasted for, at least, $\sim$3-4 Gyr and ended about 10 Gyr ago, its metallicities ranging from $-$1.7 to $-$0.8. We categorise these populations into two main epochs: the evolution of GSE in isolation and the merger event. This separation finds independent support from the age-metallicty relation of GSE globular clusters (Aguado-Agelet et al., subm.). The fourth population is younger and more metal-rich, at $\sim$8.5 Gyr and [M/H]$\sim-0.4$; its link to GSE is unclear.