Neutrinos with energies in the PeV to EeV range produce upgoing extensive air showers when they interact underground close enough to the surface of the Earth. We study the possibility for detection of such showers with a system of very wide field-of-view imaging atmospheric Cherenkov telescopes, named CHANT for CHerenkov from Astrophysical Neutrinos Telescope, pointing down to a strip below the Earth's horizon from space. We find that CHANT provides sufficient sensitivity for the study of the astrophysical neutrino flux in a wide energy range, from 10~PeV to 10~EeV. A space-based CHANT system can discover and study in detail the cosmogenic neutrino flux originating from interactions of ultra-high-energy cosmic rays in the intergalactic medium.
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