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A Warning on the GeV-TeV Connection in Blazars

Fermi-LAT spectra at high energies (HE, 0.1-100 GeV) are often extrapolated to very high energies (VHE, >100 GeV) and considered either a good estimate or an upper limit for the blazars intrinsic VHE spectrum. This assumption seems not well justified, neither theoretically nor observationally. Besides being often softer, observations do indicate that spectra at VHE could be also harder than at HE, even when adopting the limit of Gamma=1.5. Results based on such straightforward GeV-TeV extrapolations are in general not reliable, and should be considered with caution.