  Weak lensing of high-redshift Type Ia supernovae induces an external
dispersion in their observed standard candle brightnesses, comparable in
magnitude to the intrinsic dispersion for redshifts z>1. The same matter
fluctuations responsible for the magnification of distant supernovae also
generate shear in the images of background galaxies. We investigate the
possibility of using lensing shear maps constructed from galaxies surrounding
the supernovae as a means of correcting the lensing-induced magnification
dispersion. We find that a considerable fraction of the lensing dispersion
derives from sub-arcminute scales, which are not probed by shear maps smoothed
on arcminute scales. We thus find that weak lensing shear maps will be of only
limited value in reducing the weak lensing magnification fluctuations of
supernovae.
