  Ultraviolet spectroscopy provides unique insights into the structure of
matter with applications ranging from fundamental tests to photochemistry in
the earth's atmosphere and astronomical observations from space telescopes. At
longer wavelengths, dual-comb spectroscopy with two interfering laser frequency
combs has evolved into a powerful technique that can offer simultaneously a
broad spectral range and very high resolution. Here we demonstrate a
photon-counting approach that can extend the unique advantages of this method
into ultraviolet regions where nonlinear frequency-conversion tends to be very
inefficient. Our spectrometer, based on two frequency combs of slightly
different repetition frequencies, provides broad span, high resolution,
frequency calibration within the accuracy of an atomic clock, and overall
consistency of the spectra. We demonstrate a signal-to-noise ratio at the
quantum limit and optimal use of the measurement time, provided by the
multiplex recording of all spectral data on a single photo-counter. Our initial
experiments are performed in the near-ultraviolet and in the visible spectral
ranges with alkali-atom vapor, with a power per comb line as low as a
femtowatt. This crucial step towards precision broadband spectroscopy at short
wavelengths clears the path to extreme-ultraviolet dual-comb spectroscopy and,
more generally, generates a new realm of applications for diagnostics at photon
level, as encountered e.g., when driving single atoms or molecules.
