  We derive the local stellar formation history from the Gaia-defined 40 pc
white dwarf sample. This is currently the largest volume-complete sample of
white dwarfs for which spectroscopy is available, allowing for classification
of the chemical abundances at the photosphere, and subsequently accurate
determination of the atmospheric parameters. We create a population synthesis
model and show that a uniform stellar formation history for the last ~10.5 Gyr
provides a satisfactory fit to the observed distribution of absolute Gaia G
magnitudes. To test the robustness of our derivation, we vary various
assumptions in the population synthesis model, including the initial mass
function, initial-to-final mass relation, kinematic evolution, binary fraction
and white dwarf cooling timescales. From these tests, we conclude that the
assumptions in our model have an insignificant effect on the derived relative
stellar formation rate as a function of look-back time. However, the onset of
stellar formation (age of Galactic disc) is sensitive to a variety of input
parameters including the white dwarf cooling models. Our derived stellar
formation history gives a much better fit to the absolute Gaia G magnitudes
than most previous studies.
