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A brief review of the results for the total cross section \sigma^{\nu N} ofultrahigh-energy neutrino deep inelastic scattering on isoscalar nucleartargets is presented. These results are based on simple approximations for\sigma^{\nu N} and are compared with the experimental data of the IceCubeCollaboration. The total cross section \sigma^{\nu N} is proportional to thestructure function F_2^{\nu N}(M_V^2/s,M_V^2), where M_V is the intermediateboson mass and s is square of the energy of the center of mass. The coefficientin the front of F_2^{\nu N}(M_V^2/s,M_V^2) depends on the asymptotic behaviorof F_2^{\nu N} at low values of x. It contains an additional term \sim \ln{s}if F_2^{\nu N} is scaled by the power \ln(1/x). Therefore, the asymptoticbehavior of F_2^{\nu N}\propto\ln^2(1/x) for small x often assumed in theliterature already leads to violation of the Froissart bound for \sigma^{\nuN}.

On ultrahigh-energy neutrino-nucleon deep-inelastic scattering and the Froissart bound