Accurate parallaxes from Gaia DR1 (TGAS) are combined with GALEX visual Nuv magnitudes to produce absolute MNUV magnitudes and an ultraviolet HR diagram for a large sample of astrometric stars. A functional fit is derived of the lower envelope main sequence of the nearest 1403 stars (distance <40pc), which should be reddening-free. Using this empirical fit, 50 nearby stars are selected with significant Nuv excess. These are predominantly late K and early M dwarfs, often associated with X-ray sources, and showing other manifestations of magnetic activity. The sample may include systems with hidden white dwarfs, stars younger than the Pleiades, or, most likely, tight interacting binaries of the BY Dra-type. A separate collection of 40 stars with precise trigonometric parallaxes and Nuv-G colors bluer than 2mag is presented. It includes several known novae, white dwarfs, and binaries with hot subdwarf (sdOB) components, but most remain unexplored.