Spectroscopy of the first resolved strongly lensed Type Ia supernova
  iPTF16geu
  We report the results from spectroscopic observations of the multiple images
of the strongly lensed Type Ia supernova (SN Ia), iPTF16geu, obtained with
ground based telescopes and the Hubble Space Telescope (HST). From a single
epoch of slitless spectroscopy with HST, we can resolve spectra of individual
lensed supernova images for the first time. This allows us to perform an
independent measurement of the time-delay between the two brightest images,
$\Delta t = 1.4 \pm 5.0$ days, which is consistent with the time-delay measured
from the light-curves.
  We also present measurements of narrow emission and absorption lines
characterizing the interstellar medium in the host galaxy at z=0.4087, as well
as in the foreground lensing galaxy at z=0.2163. We detect strong Na ID
absorption in the host galaxy, indicating that iPTF16geu belongs to a subclass
of SNe Ia displaying "anomalously" large Na ID column densities in comparison
to the amount of dust extinction derived from their light curves. For the
deflecting galaxy, we refine the measurement of the velocity dispersion,
$\sigma = 129 \pm 4$ km/s, which significantly constrains the lens model.
  Since the time-delay between the SN images is negligible, we can use
unresolved ground based spectroscopy, boosted by a factor ~70 from lensing
magnification, to study the properties of a high-z SN Ia with unprecedented
signal-to-noise ratio. The spectral properties of the supernova, such as
pseudo-Equivalent widths of several absorption features and velocities of the
Si II-line indicate that iPTF16geu, besides being lensed, is a normal SN Ia,
indistinguishable from well-studied ones in the local universe, providing
support for the use of SNe Ia in precision cosmology. We do not detect any
significant deviations of the SN spectral energy distribution from microlensing
of the SN photosphere by stars and compact objects in the lensing galaxy.
