Type Ia Supernovae and Q 0

Type Ia Supernovae hold great promise to measure the cosmic deceleration. The diversity observed among these explosions, however , complicates their ability to measure cosmological parameters considerably. The comparison of near and distant objects depends critically on the global properties of the samples. Systematic errors are introduced in cases where the samples are not compatible. Our discussion of systematic uncertainties emphasizes the dependence on the zero-point defined by the nearby SNe Ia sample and the influence of the application of light curve corrections to the luminosity. Other error sources are in principle controllable. We illustrate the effects in an analysis of four SNe Ia at z > 0.4.