  Abelian vector fields non-minimally coupled to uncharged scalar fields arise
in many contexts. We investigate here through algebraic methods their
consistent deformations ("gaugings"), i.e., the deformations that preserve the
number (but not necessarily the form or the algebra) of the gauge symmetries.
Infinitesimal consistent deformations are given by the BRST cohomology classes
at ghost number zero. We parametrize explicitly these classes in terms of
various types of global symmetries and corresponding Noether currents through
the characteristic cohomology related to antifields and equations of motion.
The analysis applies to all ghost numbers and not just ghost number zero. We
also provide a systematic discussion of the linear and quadratic constraints on
these parameters that follow from higher-order consistency. Our work is
relevant to the gaugings of extended supergravities.
