  We present cosmological parameter measurements from the effective field
theory-based full-shape analysis of the power spectrum of emission line
galaxies (ELGs). First, we perform extensive tests on simulations and determine
appropriate scale cuts for the perturbative description of the ELG power
spectrum. We study in detail non-linear redshift-space distortions
(``fingers-of-God'') for this sample and show that they are somewhat weaker
than those of luminous red galaxies. This difference is not significant for
current data, but may become important for future surveys like Euclid/DESI.
Then we analyze recent measurements of the ELG power spectrum from the extended
Baryon acoustic Oscillation Spectroscopic Survey (eBOSS) within the
$\nu\Lambda$CDM model. Combined with the BBN baryon density prior, the ELG pre-
and post-reconstructed power spectra alone constrain the matter density
$\Omega_m=0.257_{-0.045}^{+0.031}$, the current mass fluctuation amplitude
$\sigma_8=0.571_{-0.076}^{+0.052}$, and the Hubble constant
$H_0=84.5_{-7}^{+5.8}$ km/s/Mpc (all at 68\% CL). Combining with other
full-shape and BAO data we measure $\Omega_m=0.327_{-0.016}^{+0.014}$,
$\sigma_8=0.69_{-0.045}^{+0.038}$, and $H_0=68.6_{-1.1}^{+1}$ km/s/Mpc. The
total neutrino mass is constrained to be $M_{\rm tot}<0.63$ eV (95\% CL) from
the BBN, full-shape and BAO data only. Finally, we discuss the apparent $\sim
3\sigma$ discrepancy in the inferred clustering amplitude between our full
shape analysis and the cosmic microwave background data.
