  We present full-sky maps of the cosmic microwave background (CMB) and
polarized synchrotron and thermal dust emission, derived from the third set of
Planck frequency maps. These products have significantly lower contamination
from instrumental systematic effects than previous versions. The methodologies
used to derive these maps follow those described in earlier papers, adopting
four methods (Commander, NILC, SEVEM, and SMICA) to extract the CMB component,
as well as three methods (Commander, GNILC, and SMICA) to extract astrophysical
components. Our revised CMB temperature maps agree with corresponding products
in the Planck 2015 delivery, whereas the polarization maps exhibit
significantly lower large-scale power, reflecting the improved data processing
described in companion papers; however, the noise properties of the resulting
data products are complicated, and the best available end-to-end simulations
exhibit relative biases with respect to the data at the few percent level.
Using these maps, we are for the first time able to fit the spectral index of
thermal dust independently over 3 degree regions. We derive a conservative
estimate of the mean spectral index of polarized thermal dust emission of
beta_d = 1.55 +/- 0.05, where the uncertainty marginalizes both over all known
systematic uncertainties and different estimation techniques. For polarized
synchrotron emission, we find a mean spectral index of beta_s = -3.1 +/- 0.1,
consistent with previously reported measurements. We note that the current data
processing does not allow for construction of unbiased single-bolometer maps,
and this limits our ability to extract CO emission and correlated components.
The foreground results for intensity derived in this paper therefore do not
supersede corresponding Planck 2015 products. For polarization the new results
supersede the corresponding 2015 products in all respects.
