Feedback processes play a fundamental role in the regulation of the star formation (SF) activity in galaxies and, in particular, in the quenching of early-type galaxies (ETGs) as has been inferred by observational and numerical studies of Lambda CDM models. At z = 0, ETGs exhibit well-known fundamental scaling relations, but the connection between them and the physical processes shaping ETG evolution remains unknown.This work aims at studying the impact of the energetic feedback due to active galactic nuclei (AGN) on the formation and evolution of ETGs.We focus on assessing the impact of AGN feedback on the evolution of the mass-plane and the fundamental plane (FP, defined by using mass surface density) as well as on morphology, kinematics, and stellar age across the FP.The Horizon-AGN and Horizon-noAGN cosmological hydrodynamical simulations were performed with identical initial conditions and including the same physical processes except for the activation of the AGN feedback in the former. We select a sample of central ETGs from both simulations using the same criteria and exhaustively study their SF activity, kinematics, and scaling relations for z <= 3. We find that Horizon-AGN ETGs identified at z = 0 follow the observed fundamental scaling relations (mass-plane, FP, mass-size relation) and qualitatively reproduce kinematic features albeit conserving a rotational inner component with a mass fraction regulated by the AGN feedback. AGN feedback seems to be required to reproduce the bimodality in the spin parameter distribution reported by observational works and the mass-size relation (with more massive galaxies having older stellar populations (SPs), larger sizes, and being slower rotators). We study the evolution of the fundamental relations with redshift, finding .Abridged
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