The white dwarf luminosity function is an important tool to understand the
properties of the Solar neighborhood, like its star formation history, and its
age. Here we present a population synthesis study of the white dwarf population
within 40~pc from the Sun, and compare the results of this study with the
properties of the observed sample. We use a state-of-the-art population
synthesis code based on Monte Carlo techniques, that incorporates the most
recent and reliable white dwarf cooling sequences, an accurate description of
the Galactic neighborhood, and a realistic treatment of all the known
observational biases and selection procedures. We find a good agreement between
our theoretical models and the observed data. In particular, our simulations
reproduce a previously unexplained feature of the bright branch of the white
dwarf luminosity function, which we argue is due to a recent episode of star
formation. We also derive the age of the Solar neighborhood employing the
position of the observed cut-off of the white dwarf luminosity function,
obtaining ~8.9+-0.2 Gyr. We conclude that a detailed description of the
ensemble properties of the population of white dwarfs within 40pc of the Sun
allows us to obtain interesting constraints on the history of the Solar
neighborhood.Comment: 8 pages, 7 figures, accepted for publication in A&