Recent observations of protoplanetary disks have revealed ring-like structures that can be associated to pressure maxima. Pressure maxima are known to be dust collectors and planet migration traps. Most of planet formation works are based either on the pebble accretion model or on the planetesimal accretion model. However, recent studies proposed the possible formation of Jupiter by the hybrid accretion of pebbles and planetesimals. We aim to study the full process of planet formation consisting of dust evolution, planetesimal formation and planet growth at a pressure maximum in a protoplanetary disk. We compute, through numerical simulations, the gas and dust evolution, including dust growth, fragmentation, radial drift and particle accumulation at a pressure bump. We also consider the formation of planetesimals by streaming instability and the formation of a moon-size embryo that grows into a giant planet by the hybrid accretion of pebbles and planetesimals. We find that pressure maxima in protoplanetary disks are efficient collectors of dust drifting inwards. The condition of planetesimal formation by streaming instability is fulfilled due to the large amount of dust accumulated at the pressure bump. Then, a massive core is quickly formed (in $sim 10^4$ yr) by the accretion of pebbles. After the pebble isolation mass is reached, the growth of the core slowly continues by the accretion of planetesimals. The energy released by planetesimal accretion delays the onset of runaway gas accretion, allowing a gas giant to form after $sim$1 Myr of disk evolution. The pressure maximum also acts as a migration trap. Pressure maxima in protoplanetary disks are preferential locations for dust traps, planetesimal formation by streaming instability and planet migration traps. All these conditions allow the fast formation of a giant planet by the hybrid accretion of pebbles and planetesimals.
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