  We present the first extensive spectroscopic study of the global population
in star clusters Trumpler~16, Trumpler~14 and Collinder~232 in the Carina
Nebula, using data from the Gaia-ESO Survey, down to solar-mass stars. In
addition to the standard homogeneous Survey data reduction, a special
processing was applied here because of the bright nebulosity surrounding Carina
stars. We find about four hundred good candidate members ranging from OB types
down to slightly sub-solar masses. About one-hundred heavily-reddened
early-type Carina members found here were previously unrecognized or poorly
classified, including two candidate O stars and several candidate Herbig Ae/Be
stars. Their large brightness makes them useful tracers of the obscured Carina
population. The spectroscopically-derived temperatures for nearly 300 low-mass
members allows the inference of individual extinction values, and the study of
the relative placement of stars along the line of sight. We find a complex
spatial structure, with definite clustering of low-mass members around the most
massive stars, and spatially-variable extinction. By combining the new data
with existing X-ray data we obtain a more complete picture of the
three-dimensional spatial structure of the Carina clusters, and of their
connection to bright and dark nebulosity, and UV sources. The identification of
tens of background giants enables us also to determine the total optical depth
of the Carina nebula along many sightlines. We are also able to put constraints
on the star-formation history of the region, with Trumpler~14 stars found to be
systematically younger than stars in other sub-clusters. We find a large
percentage of fast-rotating stars among Carina solar-mass members, which
provide new constraints on the rotational evolution of pre-main-sequence stars
in this mass range.
