  So far, the Sun is the only isolated main sequence star detected in
gamma-rays, particularly during powerful flares. Young ultracool dwarfs are far
more active so they are also plausible gamma-ray sources. We performed a
spatial stack of 97 of the nearest X-ray and radio flare stars to search for
GeV emission using nearly 12 years of data from the Fermi Gamma-ray Space
Telescope. The stacked residual maps showed no significant signal. Modeling the
upper limits indicates a peak stellar flux at least a factor of 7 below the
noise level. We also analyzed the phase-folded light curve of the rapidly
rotating radio star TVLM 513-46546, report a tentative (TS = 30) pulsed signal,
and refine its period. We examine the possibility of a false positive signal by
analyzing nearby Fermi catalog sources and test fields, and by repeating the
analysis using different periods. No other periodic signals are found, despite
clear detections of the catalog sources, and the TS value for TVLM 513
increases systematically to the optimal period. The putative gamma-ray signal
is nearly in phase with the optical peak, and out of phase with the radio
pulses by 0.4 +/- 0.05 rotations. These results argue for emission from
relativistic protons streaming down flux tubes towards the photospheric active
regions. The protons colliding with the atmosphere create neutral pions that
decay into gamma-ray photons. This would be the first detection of a normal,
isolated star in gamma-rays, and the strongest evidence yet for proton
acceleration in stellar magnetospheres.
