Mapping the Universe with slitless spectroscopy

Euclid will survey most of the accessible extragalactic sky with imaging and slitless spectroscopy observations, creating a unique spectroscopic catalog of galaxies with H$\alpha$ line in emission that will map the Universe from $z=0.9$ to $1.8$. With low expected statistical errors, the error budget will likely be dominated by systematic errors related to uncertainties in the data and modelling. I will discuss the strategy that has been proposed to mitigate the expected systematic effects and propagate the uncertainty of mitigation to cosmological parameter errobars.