The ALMA-CRISTAL survey: Resolved kinematic studies of main sequence star-forming galaxies at 4

̊m M_⊙ ),łeqslant,$10.9$) main sequence star-forming galaxies (MS SFGs) at $4$,$<$,z,$<$,$6$ from the ALMA-CRISTAL programme. The data consist of deep (up to 15,hr observing time per target), high-resolution (∼,$1$kpc) ALMA observations of C II 158μm line emission. This dataset allowed us to carry out the first systematic, kiloparsec-scale (kpc-scale) characterisation of the kinematics nature of typical massive SFGs at these epochs. We find that ∼,$50%$ of the sample are disk-like, with a number of galaxies located in systems of multiple components. Kinematic modelling reveals these main sequence disks exhibit high-velocity dispersions (σ_0), with a median disk velocity dispersion of ∼,$70,$$ $ and V_ ̊m rot /σ_0,∼,$2$, which is consistent with dominant gravity driving. The elevated disk dispersions are in line with the predicted evolution based on Toomre theory and the extrapolated trends from z∼0--$2.5$ MS star-forming disks. The inferred dark matter (DM) mass fraction within the effective radius f_ ̊m DM (<R_ ̊m e ) for the disk systems decreases with the central baryonic mass surface density. This is consistent with the trend reported by kinematic studies at złesssim3; roughly half the disks display f_ ̊m DM (<R_ ̊m e )łesssim,$ $. The CRISTAL sample of massive MS SFGs provides a reference of the kinematics of a representative population and extends the view onto typical galaxies beyond previous kpc-scale studies at złesssim3.