  We present the results of a high-resolution, 5 GHz, Karl G. Jansky Very Large
Array study of the nuclear radio emission in a representative subset of the
Atlas3D survey of early-type galaxies (ETGs). We find that 51 +/- 4% of the
ETGs in our sample contain nuclear radio emission with luminosities as low as
10^18 W/Hz. Most of the nuclear radio sources have compact (< 25-110 pc)
morphologies, although < 10% display multi-component core+jet or extended
jet/lobe structures. Based on the radio continuum properties, as well as
optical emission line diagnostics and the nuclear X-ray properties, we conclude
that the majority of the central 5 GHz sources detected in the Atlas3D galaxies
are associated with the presence of an active galactic nucleus (AGN). However,
even at sub-arcsecond spatial resolution, the nuclear radio emission in some
cases appears to arise from low-level nuclear star formation rather than an
AGN, particularly when molecular gas and a young central stellar population is
present. This is in contrast to popular assumptions in the literature that the
presence of a compact, unresolved, nuclear radio continuum source universally
signifies the presence of an AGN. Additionally, we examine the relationships
between the 5 GHz luminosity and various galaxy properties including the
molecular gas mass and - for the first time - the global kinematic state. We
discuss implications for the growth, triggering, and fueling of radio AGNs, as
well as AGN-driven feedback in the continued evolution of nearby ETGs.
