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Context.Stars with initial mass above roughly 8M_⊙will evolve to form a core made of iron group elements, at which point no further exothermic nuclear reactions between charged nuclei may prevent the core collapse. Electron capture, neutrino losses, and the photo-disintegration of heavy nuclei trigger the collapse of these stars. Models at the brink of core collapse are produced using stellar evolution codes, and these pre-collapse models may be used in the study of the subsequent dynamical evolution (including their explosion as supernovae and the formation of compact remnants such as neutron stars or black holes). Aims.We upgraded the physical ingredients employed by the GENeva stellar Evolution Code, GENEC, so that it covers the regime of high-temperatures and high-densities required to produce the progenitors of core-collapse. Our ultimate goal is producing pre-supernova models with GENEC, not only right before collapse, but also during the late phases (silicon and oxygen burning). Methods.We have improved GENEC in three directions: equation of state, the nuclear reaction network, and the radiative and conductive opacities adapted for the computation of the advanced phases of evolution. We produce a small grid of pre-supernova models of stars with zero age main sequence masses of 15 M_⊙, 20 M_⊙, and 25 M_⊙at solar and less than half solar metallicities. The results are compared with analogous models produced with the MESA code. Results.The global properties of our new models, particularly of their inner cores, are comparable to models computed with MESA and pre-existing progenitors in the literature. Between codes the exact shell structure varies, and impacts explosion predictions. Conclusions.Using GENEC with state-of-the-art physics, we have produced massive stellar progenitors prior to collapse. These progenitors are suitable for follow-up studies, including the dynamical collapse and supernova phases. Larger grids of supernova progenitors are now feasible, with the potential for further dynamical evolution. 

Context.Grids of stellar evolution models with rotation using the Geneva stellar evolution code (GENEC) have been published for a wide range of metallicities. Aims.We introduce the last remaining grid of GENECmodels, with a metallicity ofZ = 10⁻⁵. We study the impact of this extremely metal-poor initial composition on various aspects of stellar evolution, and compare it to the results from previous grids at other metallicities. We provide electronic tables that can be used to interpolate between stellar evolution tracks and for population synthesis. Methods.Using the same physics as in the previous papers of this series, we computed a grid of stellar evolution models with GENECspanning masses between 1.7 and 500M_⊙, with and without rotation, at a metallicity ofZ = 10⁻⁵. Results.Due to the extremely low metallicity of the models, mass-loss processes are negligible for all except the most massive stars. For most properties (such as evolutionary tracks in the Hertzsprung-Russell diagram, lifetimes, and final fates), the present models fit neatly between those previously computed at surrounding metallicities. However, specific to this metallicity is the very large production of primary nitrogen in moderately rotating stars, which is linked to the interplay between the hydrogen- and helium-burning regions. Conclusions.The stars in the present grid are interesting candidates as sources of nitrogen-enrichment in the early Universe. Indeed, they may have formed very early on from material previously enriched by the massive short-lived Population III stars, and as such constitute a very important piece in the puzzle that is the history of the Universe.