The first Fermi-LAT Catalog of sources above 10 GeV

We present a catalog of gamma-ray sources at energies above 10 GeV based on data from the Large Area Telescope (LAT) accumulated during the first 3 yr of the Fermi Gamma-ray Space Telescope mission. The first Fermi catalog of > 10 GeV sources (1FHL) has 514 sources. For each source we present location, spectrum, a measure of variability, and associations with cataloged sources at other wavelengths. We found that 449 (87%) could be associated with known sources, of which 393 (76% of the 1FHL sources) are active galactic nuclei. Of the 27 sources associated with known pulsars, we find 20 (12) to have significant pulsations in the range > 10 GeV (> 25 GeV). In this work we also report that, at energies above 10 GeV, unresolved sources account for 27% +/- 8% of the isotropic. gamma-ray background, while the unresolved Galactic population contributes only at the few percent level to the Galactic diffuse background. We also highlight the subset of the 1FHL sources that are best candidates for detection at energies above 50-100 GeV with current and future ground-based gamma-ray observatories.