  In order to investigate the role of gas in the demise of star formation on
kpc-scales, we compare the resolved molecular gas main sequence (rMGMS: Sigma_*
vs Sigma_H2) of star-forming regions to the sequence of `retired' regions that
have ceased to form new stars. Using data from the ALMaQUEST survey, we find
that retired spaxels form a rMGMS that is distinct from that of star-forming
spaxels, offset to lower Sigma_H2 at fixed Sigma_* by a factor of ~5. We study
the rMGMS of star-forming and retired spaxels on a galaxy-by-galaxy basis for
eight individual ALMaQUEST galaxies. Six of these galaxies have their retired
spaxels concentrated within the central few kpc. Molecular gas is detected in
40-100% of retired spaxels in the eight galaxies in our sample. Both the
star-forming and retired rMGMS show a diversity in normalization from
galaxy-to-galaxy. However, in any given galaxy, the rMGMS for retired regions
is found to be distinct from the star-forming sequence and gas fractions of
retired spaxels are up to an order of magnitude lower than the star-forming
spaxels. We conclude that quenching is associated with a depletion (but not
absence) of molecular gas via a mechanism that typically begins in the centre
of the galaxy.
