By using updated stellar low-mass stars models, we systematically investigate the nucleosynthesis processes occurring in asymptotic giant branch (AGB) stars. In this paper, we present a database dedicated to the nucleosynthesis of AGB stars: FRANEC Repository of Updated Isotopic Tables & Yields (FRUITY). An interactive Web-based interface allows users to freely download the full (from H to Bi) isotopic composition, as it changes after each third dredge-up (TDU) episode and the stellar yields the models produce. A first set of AGB models, having masses in the range 1.5 ⩽ M / M ☉ ⩽ 3.0 and metallicities 1 × 10 −3 ⩽ Z ⩽ 2 × 10 −2 , is discussed. For each model, a detailed description of the physical and the chemical evolution is provided. In particular, we illustrate the details of the s -process and we evaluate the theoretical uncertainties due to the parameterization adopted to model convection and mass loss. The resulting nucleosynthesis scenario is checked by comparing the theoretical [hs/ls] and [Pb/hs] ratios to those obtained from the available abundance analysis of s -enhanced stars. On the average, the variation with the metallicity of these spectroscopic indexes is well reproduced by theoretical models, although the predicted spread at a given metallicity is substantially smaller than the observed one. Possible explanations for such a difference are briefly discussed. An independent check of the TDU efficiency is provided by the C-stars luminosity function. Consequently, theoretical C-stars luminosity functions for the Galactic disk and the Magellanic Clouds have been derived. We generally find good agreement with observations.
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