  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.
