The evolution of stellar mass and the implied star formation history

We present a compilation of measurements of the stellar mass density as a function of redshift. Using this stellar mass history we obtain a star formation history and compare it to the instantaneous star formation history. For z < 0.7 there is good agreement between the two star formation histories. At higher redshifts the instantaneous indicators suggest star formation rates larger than that implied by the evolution of the stellar mass density. This discrepancy peaks at z= 3 where instantaneous indicators suggest a star formation rate around 0.6 dex higher than those of the best fit to the stellar mass history. We discuss a variety of explanations for this inconsistency, such as inaccurate dust extinction corrections, incorrect measurements of stellar masses and a possible evolution of the stellar initial mass function.