  We use spin-density-functional theory within an envelope function approach to
calculate electronic states in a GaAs/InAs core-shell nanowire pierced by an
axial magnetic field. Our fully 3D quantum modeling includes explicitly the
description of the realistic cross-section and composition of the sample, and
the electrostatic field induced by external gates in two different device
geometries, gate-all-around and back-gate. At low magnetic fields, we
investigate Aharonov-Bohm oscillations and signatures therein of the discrete
symmetry of the electronic system, and we critically analyze recent
magnetoconductance observations. At high magnetic fields we find that several
charge and spin transitions occur. We discuss the origin of these transitions
in terms of different localization and Coulomb regimes and predict their
signatures in magnetoconductance experiments.
