Tau neutrinos with energies in the PeV-EeV range produce up-going extensive air showers (UEAS) if they interact underground close enough to the surface of the Earth. This work studies detectability of the UEAS with a system of fluorescence telescopes overlooking dark, low reflectivity, area on the ground up to the distances 20-30 km from mountain top(s). Such system could provide sensitivity sufficient for accumulation of the astrophysical neutrino signal statistics at the rate ten(s) events per year in the energy range beyond 10 PeV, thus allowing to extend the energy frontier of neutrino astronomy into 10-100 PeV range. Comparison of sensitivities of the top-of-the-mountain telescope and IceCube Generation II shows that the two approaches for neutrino detection are complementary, providing comparable performance in adjacent energy bands below and above 10~PeV. Sensitivity of the top-of-the-mountain fluorescence telescope system is also sufficient for the discovery of theoretically predicted cosmogenic neutrino signal.
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