In order to provide a better basis for the study of mechanisms of nucleosynthesis of the light elements beyond hydrogen and helium in the oldest stars, the abundances of C, O, Mg, Si, P, S, K, and Ca have been derived from UV-HST and visible-ESO high resolution spectra in the old, very metal-poor star HD 84937, at a metallicity that is 1/200 that of the Suns. For this halo main-sequence turnoff star, the abundance determination of P and S are the first published determinations. The LTE profiles of the lines were fitted to the observed spectra. Wherever possible, we corrected the derived abundances for non-LTE effects. Three-dimensional (3D) CO5BOLD model atmospheres have been used to determine the abundances of C and O from molecular CH and OH bands. The abundances of these light elements in HD 84937 are found to agree well with the abundances in classical metal-poor stars. Our HD 84937 carbon abundance determination points toward a solar (or mildly enhanced) value of [C/Fe]. The modest overabundance of the alpha elements of even atomic number Z, typical of halo turnoff stars, is confirmed in this example. The odd-Z element P is found to be somewhat deficient in HD 84937, at [P/Fe]=-0.32, which is again consistent with the handful of existing determinations for turnoff stars of such low metallicity. We show that the abundance of oxygen, deduced from the OH band from 3D computations, is not compatible with the abundance deduced from the red oxygen triplet. This incompatibility is explained by the existence of a chromosphere heating the shallow layers of the atmosphere where the OH band, in 3D computations, is mainly formed. The abundance ratios are compared to the predictions of models of galactic nucleosynthesis and evolution
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