Context : The Sagittarius B2 molecular cloud contains several sites forming high-mass stars .
Sgr B2 ( N ) is one of its main centers of activity .
It hosts several compact and ultra-compact HII regions , as well as two known hot molecular cores ( Sgr B2 ( N1 ) and Sgr B2 ( N2 ) ) in the early stage of the high-mass star formation process , where complex organic molecules ( COMs ) are detected in the gas phase .

Aims : Our goal is to use the high sensitivity of the Atacama Large Millimeter/submillimeter Array ( ALMA ) to characterize the hot core population in Sgr B2 ( N ) and thereby shed a new light on the star formation process in this star-forming region .

Methods : We use a complete 3 mm spectral line survey conducted with ALMA to search for faint hot cores in the Sgr B2 ( N ) region .
The chemical composition of the detected sources and the column densities are derived by modelling the whole spectra under the assumption of local thermodynamic equilibrium .
Population diagrams are constructed to fit rotational temperatures .
Integrated intensity maps are produced to derive the peak position and fit the size of each molecule ’ s emission distribution .
The kinematic structure of the hot cores is investigated by analyzing the line wing emission of typical outflow tracers .
The H _ { 2 } column densities are computed from ALMA and SMA continuum emission maps .

Results : We report the discovery of three new hot cores in Sgr B2 ( N ) that we call Sgr B2 ( N3 ) , Sgr B2 ( N4 ) , and Sgr B2 ( N5 ) .
The three sources are associated with class II methanol masers , well known tracers of high-mass star formation , and Sgr B2 ( N5 ) also with a UCHII region .
Their H _ { 2 } column densities are found to be \sim 16 up to 36 times lower than the one of the main hot core Sgr B2 ( N1 ) .
The spectra of these new hot cores have spectral line densities of 11 up to 31 emission lines per GHz above the 7 \sigma level , assigned to 22–25 molecules plus 13–20 less abundant isotopologs .
We derive rotational temperatures around 140–180 K for the three new hot cores and mean source sizes of 0.4 \arcsec for Sgr B2 ( N3 ) and 1.0 \arcsec for Sgr B2 ( N4 ) and Sgr B2 ( N5 ) .
The chemical composition of Sgr B2 ( N3 ) , Sgr B2 ( N4 ) , and Sgr B2 ( N5 ) is very similar , but it differs from that of Sgr B2 ( N2 ) .
Finally , Sgr B2 ( N3 ) and Sgr B2 ( N5 ) show high velocity wing emission in typical outflow tracers , with a bipolar morphology in their integrated intensity maps suggesting the presence of an outflow , like in Sgr B2 ( N1 ) .
No sign of an outflow is found around Sgr B2 ( N2 ) and Sgr B2 ( N4 ) .
We derive statistical lifetimes of 4 \times 10 ^ { 4 } yr for the class II methanol maser phase and 6 \times 10 ^ { 4 } yr for the hot core phase in Sgr B2 ( N ) .

Conclusions : The associations of the hot cores with class II methanol masers , outflows , and/or UCHII regions tentatively suggest the following age sequence : Sgr B2 ( N4 ) , Sgr B2 ( N3 ) , SgrB2 ( N5 ) , Sgr B2 ( N1 ) .
The status of Sgr B2 ( N2 ) is unclear .
It may contain two distinct sources , a UCHII region and a very young hot core .