  Neutrino telescopes like IceCube, KM3NeT and Baikal-GVD offer physicists the
opportunity to study neutrinos with energies far beyond the reach of
terrestrial accelerators. These neutrinos are used to study high-energy
neutrino interactions and to probe the Earth through absorption tomography.
Current studies of TeV neutrinos use cross sections which are calculated for
free nucleons with targets which are assumed to contain equal numbers of
protons and neutrons.
  Here we consider modifications of high-energy neutrino interactions due to
two nuclear effects: modifications of the parton densities in the nucleus,
referred to here as shadowing, and the effect of non-isoscalar targets, with
unequal numbers of neutrons and protons. Both these effects depend on the
interaction medium. Because shadowing is larger for heavier nuclei, such as
iron, found in the Earth's core, it introduces a zenith-angle dependent change
in the absorption cross section. These modifications increase the cross
sections by 1-2\% at energies below 100 TeV (antishadowing), and reduce it by
3-4\% at higher energies (shadowing).
  Nuclear effects also alter the inelasticity distribution of neutrino
interactions in water/ice by increasing the number of low inelasticity
interactions, with a larger effect for $\nu$ than $\bar\nu$. These effects are
particularly large in the energy range below a few TeV. These effects could
alter the cross sections inferred from events with tracks originating within
the active detector volume as well as the ratio $\nu/\bar\nu$ inferred from
inelasticity measurements.
  The uncertainties in these nuclear effects are larger than the uncertainties
on the free-proton cross sections and will thus limit the systematic precision
of future high-precision measurements at neutrino telescopes.

High Energy Physics - Phenomenology;High Energy Astrophysical Phenomena;Nuclear Experiment;Nuclear Theory