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The Gaia-ESO Survey (GES) observed many open clusters as part of its programme to spectroscopically characterize the various Milky Way populations. GES spectroscopy and Gaia astrometry from its second data release are used here to assign membership probabilities to targets towards 32 open clusters with ages from 1 to 3800 Myr, based on maximum likelihood modelling of the 3D kinematics of the cluster and field populations. From a parent catalogue of 14 398 individual targets, 5032 stars with uniformly determined 3D velocities, Teff, log g, and chemistry are assigned cluster membership with probability >0.9, and with an average probability of 0.991. The robustness of the membership probabilities is demonstrated using independent membership criteria (lithium and parallax) in two of the youngest clusters. The addition of radial velocities improves membership discrimination over proper motion selection alone, especially in more distant clusters. The kinematically selected nature of the membership lists, independent of photometry and chemistry, makes the catalogue a valuable resource for testing stellar evolutionary models and investigating the time evolution of various parameters. ; This work was partly supported by the European Union FP7 programme through ERC grant number 320360 and by the Leverhulme Trust through grant no. RPG-2012-541. We acknowledge the support from INAF and Ministero dell' Istruzione, dell' Università' e della Ricerca (MIUR) in the form of the grant 'Premiale VLT 2012'. The results presented here benefit from discussions held during the Gaia-ESO workshops and conferences supported by the ESF (European Science Foundation) through the GREAT Research Network Programme. ; Peer reviewed

Context. In the era of large spectroscopic surveys, massive databases of high-quality spectra coupled with the products of the Gaia satellite provide tools to outline a new picture of our Galaxy. In this framework, an important piece of information is provided by our ability to infer stellar ages, and consequently to sketch a Galactic timeline. Aims. We aim to provide empirical relations between stellar ages and abundance ratios for a sample of stars with very similar stellar parameters to those of the Sun, namely the so-called solar-like stars. We investigate the dependence on metallicity, and we apply our relations to independent samples, that is, the Gaia-ESO samples of open clusters and of field stars. Methods. We analyse high-resolution and high-signal-to-noise-ratio HARPS spectra of a sample of solar-like stars to obtain precise determinations of their atmospheric parameters and abundances for 25 elements and/or ions belonging to the main nucleosynthesis channels through differential spectral analysis, and of their ages through isochrone fitting. Results. We investigate the relations between stellar ages and several abundance ratios. For the abundance ratios with a steeper dependence on age, we perform multivariate linear regressions, in which we include the dependence on metallicity, [Fe/H]. We apply our best relations to a sample of open clusters located from the inner to the outer regions of the Galactic disc. Using our relations, we are able to recover the literature ages only for clusters located at RGC&Rlarr2; > &Rlarr2; 7 kpc. The values that we obtain for the ages of the inner-disc clusters are much greater than the literature ones. In these clusters, the content of neutron capture elements, such as Y and Zr, is indeed lower than expected from chemical evolution models, and consequently their [Y/Mg] and [Y/Al] are lower than in clusters of the same age located in the solar neighbourhood. With our chemical evolution model and a set of empirical yields, we suggest that a strong dependence on the star formation history and metallicity-dependent stellar yields of s-process elements can substantially modify the slope of the [s/α]-[Fe/H]-age relation in different regions of the Galaxy. Conclusions. Our results point towards a non-universal relation [s/α]-[Fe/H]-age, indicating the existence of relations with different slopes and intercepts at different Galactocentric distances or for different star formation histories. Therefore, relations between ages and abundance ratios obtained from samples of stars located in a limited region of the Galaxy cannot be translated into general relations valid for the whole disc. A better understanding of the s-process at high metallicity is necessary to fully understand the origin of these variations. © ESO 2020. ; The authors would like to thanks Dr. Leslie K. Hunt for her help in the statistical interpretation of our results. Based on data products from observations made with ESO Telescopes at the La Silla Paranal Observatory under programme ID 188.B-3002. These data products have been processed by the Cambridge Astronomy Survey Unit (CASU) at the Institute of Astronomy, University of Cambridge, and by the FLAMES/UVES reduction team at INAF/Osservatorio Astrofisico di Arcetri. These data have been obtained from the GES Survey Data Archive, prepared and hosted by the Wide Field Astronomy Unit, Institute for Astronomy, University of Edinburgh, which is funded by the UK Science and Technology Facilities Council (STFC). This research has made use of the services of the ESO Science Archive Facility. This work was partly supported by the European Union FP7 programme through ERC grant number 320360 and by the Leverhulme Trust through grant RPG-2012-541. We acknowledge the support from INAF and Ministero dell' Istruzione, dell' Universita e della Ricerca (MIUR) in the form of the grant "Premiale VLT 2012". The results presented here benefit from discussions held during the GES workshops and conferences supported by the ESF (European Science Foundation) through the GREAT Research Network Programme. LM acknowledge the funding from the INAF PRIN-SKA 2017 program 1.05.01.88.04. LM and MVdS acknowledge the funding from MIUR Premiale 2016: MITIC. T.B. was supported by the project grant "The New Milky Way" from the Knut and Alice Wallenberg Foundation. M. acknowledges support provided by the Spanish Ministry of Economy and Competitiveness (MINECO), under grant AYA-2017-88254-P. L.S. acknowledges financial support from the Australian Research Council (Discovery Project 170100521) and from the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013. F.J.E. acknowledges financial support from the ASTERICS project (ID:653477, H2020-EU.1.4.1.1. - Developing new world-class research infrastructures). U.H. acknowledges support from the Swedish National Space Agency (SNSA/Rymdstyrelsen). T.B was partly funded by the project grant "The New Milky Way" from the Knut and Alice Wallenberg Foundation, and partly by grant No. 2018-04857 from the Swedish Research Council. ; Peer reviewed