  The SgrB2 molecular cloud contains several sites forming high-mass stars.
SgrB2(N) is one of its main centers of activity. It hosts several compact and
UCHII regions, as well as two known hot molecular cores (SgrB2(N1) and
SgrB2(N2)), where complex organic molecules are detected. Our goal is to use
the high sensitivity of ALMA to characterize the hot core population in
SgrB2(N) and shed a new light on the star formation process. We use a complete
3 mm spectral line survey conducted with ALMA to search for faint hot cores in
SgrB2(N). We report the discovery of three new hot cores that we call
SgrB2(N3), SgrB2(N4), and SgrB2(N5). The three sources are associated with
class II methanol masers, well known tracers of high-mass star formation, and
SgrB2(N5) also with a UCHII region. The chemical composition of the sources and
the column densities are derived by modelling the whole spectra under the
assumption of LTE. The H2 column densities are computed from ALMA and SMA
continuum emission maps. The H2 column densities of these new hot cores are
found to be 16 up to 36 times lower than the one of the main hot core Sgr
B2(N1). Their spectra have spectral line densities of 11 up to 31 emission
lines per GHz, assigned to 22-25 molecules. We derive rotational temperatures
around 140-180 K for the three new hot cores and mean source sizes of 0.4 for
SgrB2(N3) and 1.0 for SgrB2(N4) and SgrB2(N5). SgrB2(N3) and SgrB2(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 SgrB2(N1). The associations of the hot cores with class II
methanol masers, outflows, and/or UCHII regions tentatively suggest the
following age sequence: SgrB2(N4), SgrB2(N3), SgrB2(N5), SgrB2(N1). The status
of SgrB2(N2) is unclear. It may contain two distinct sources, a UCHII region
and a very young hot core.
