  We present an expanded sample of 75 Milky Way Cepheids with Hubble Space
Telescope (HST) photometry and Gaia EDR3 parallaxes which we use to recalibrate
the extragalactic distance ladder and refine the determination of the Hubble
constant. All HST observations were obtained with the same instrument (WFC3)
and filters (F555W, F814W, F160W) used for imaging of extragalactic Cepheids in
Type Ia supernova (SN Ia) hosts. The HST observations used the WFC3 spatial
scanning mode to mitigate saturation and reduce pixel-to-pixel calibration
errors, reaching a mean photometric error of 5 millimags per observation. We
use new Gaia EDR3 parallaxes, vastly improved since DR2, and the
Period-Luminosity (PL) relation of these Cepheids to simultaneously calibrate
the extragalactic distance ladder and to refine the determination of the Gaia
EDR3 parallax offset. The resulting geometric calibration of Cepheid
luminosities has 1.0% precision, better than any alternative geometric anchor.
Applied to the calibration of SNe~Ia, it results in a measurement of the Hubble
constant of 73.0 +/- 1.4 km/sec/Mpc, in good agreement with conclusions based
on earlier Gaia data releases. We also find the slope of the Cepheid PL
relation in the Milky Way, and the metallicity dependence of its zeropoint, to
be in good agreement with the mean values derived from other galaxies. In
combination with the best complementary sources of Cepheid calibration, we
reach 1.8% precision and find H_0=73.2 +/- 1.3 km/sec/Mpc, a 4.2 sigma
difference with the prediction from Planck CMB observations under LambdaCDM. We
expect to reach ~1.3% precision in the near term from an expanded sample of ~40
SNe Ia in Cepheid hosts.
