Motivated by the recent challenging results from TeV astronomy, the VHE INAF community asked a group of them to write this White Paper to summarize the status and future of Cherenkov telescopes for gamma-ray astronomy and the INAF perspectives in this field. This document wants to review both the scientific topics and potential developments of the field as well as to point out both the interests and the capacities (scientific and technical) of the VHE astrophysics community in INAF. It is aimed at identifying the scientific and technological areas where INAF should focus its efforts and resources so that Italian researchers can achieve (or maintain) a leading position in this field.
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