  A cubic kilometer scale experiment has been proposed to detect cosmic
neutrinos of energy from tens of GeV up to the highest energies observed for
cosmic rays, around 10**20 eV, or possibly even beyond. Detection efficiencies
depend crucially on the neutrino-nucleon cross section at these energies at
which radiative corrections beyond the lowest order approximation could become
non-negligible. The differential cross sections can be modified by more than
50% in some regions of phase space. Estimates of corrections to the quantities
most relevant for neutrino detection at these energies give, however, less
dramatic effects: The average inelasticity in the outgoing lepton is increased
from about 0.19 to 0.24. The inclusive cross section is reduced by roughly half
a percent. The dominant uncertainty of the standard model ultra-high energy
neutrino-nucleon cross section therefore still comes from uncertainties of the
parton distributions in the nucleon at very low momentum fractions.
