  Models of the origin of astrophysical neutrinos with energies from TeVs to
PeVs are strongly constrained by multimessenger observations and population
studies. Recent results point to statistically significant associations between
these neutrinos and active galactic nuclei (AGN) selected by their radio flux
observed with very-long-baseline interferometry (VLBI). This suggests that the
neutrinos are produced in central parsecs of blazars, AGN with relativistic
jets pointing to the observer. However, conventional AGN models tend to explain
only the highest-energy part of the neutrino flux observationally associated
with blazars. Here we discuss in detail how the neutrinos can be produced in
the part of an AGN giving the dominant contribution to the VLBI radio flux, the
radio core located close to the jet base. Physical conditions there differ both
from the immediate environment of the central black hole and from the plasma
blobs moving along the jet. Required neutrino fluxes, considerably smaller than
those of photons, can be produced in interactions of relativistic protons,
accelerated closer to the black hole, with radiation in the core.
