Spatially-resolved studies of the kinematics of galaxies provide crucialinsights into their assembly and evolution, enabling to infer the properties ofthe dark matter halos, derive the impact of feedback on the ISM, characterizethe outflow motions. To date, most of the kinematic studies at z=0.5-3.5 wereobtained using emission lines tracing the warm, ionized gas. However, whetherthese provide an exhaustive or only a partial view of the dynamics of galaxiesand of the properties of the ISM is still debated. Complementary insights onthe cold gas kinematics are therefore needed. We present ALPAKA, a projectaimed at gathering high-resolution observations of CO and [CI] emission linesof star-forming galaxies at z=0.5-3.5 from the ALMA public archive. With 147hours of total integration time, ALPAKA assembles ~0.25'' observations for 28star-forming galaxies, the largest sample with spatially-resolved cold gaskinematics as traced by either CO or [CI] at z>0.5. By combiningmulti-wavelength ancillary data, we derive the stellar masses ($M_{\star}$) andstar-formation rates (SFR) for our targets, finding values of $M_{\star}\gtrsim10^{10}$ M$_{\odot}$ and SFR of 10-3000 M$_{\odot}$/yr. A large fraction ofALPAKA galaxies (19/28) lie in overdense regions (clusters, groups, andprotoclusters). We exploit the ALMA data to infer their dynamical state and wefind that 19/28 ALPAKA galaxies are rotating disks, 2 are interacting systems,while for the remaining 7 sources the classification is uncertain. The diskshave velocity dispersion values that are typically larger in the innermostregions than in the outskirts, with a median value for the entire disk sampleof 35$^{+11}_{-9}$ km/s. Despite the bias of our sample towards galaxieshosting very energetic mechanisms, the ALPAKA disks have high ratios ofordered-to-random motion ($V/\sigma$) with a median value of 9$^{+7}_{-2}$.

High-redshift galaxies are expected to be more turbulent than local galaxiesbecause of their smaller size and higher star formation and thus strongerfeedback from star formation, frequent mergers events, and gravitationalinstabilities. However, this scenario has recently been questioned by theobservational evidence of a few galaxies at z~4-5 with a gas velocitydispersion similar to what is observed in the local population. Our goal is todetermine whether galaxies in the first Gyrs of the Universe have alreadyformed a dynamically cold rotating disk similar to the local counterparts. Westudied the gas kinematic of 22 main-sequence star-forming galaxies at z > 5and determined their dynamical state by estimating the ratio of the rotationalvelocity and of the gas velocity dispersion. We mined the ALMA archive andexploited the [CII] and [OIII] observations to perform a kinematic analysis ofthe cold and warm gas of z>5 main-sequence galaxies. The gas kinematics of thehigh-z galaxies is consistent within the errors with rotating but turbulentdisks. We infer a velocity dispersion that is systematically higher by 4 timesthan the local galaxy population and the z~5 dust-obscured galaxies reported inthe literature. The difference between our results and those reported atsimilar redshift can be ascribed to the systematic difference in the galaxyproperties in the two samples: the disks of massive dusty galaxies aredynamically colder than the disks of dust-poor galaxies. The comparison withthe theoretical predictions suggests that the main driver of the velocitydispersion in high-z galaxies is the gravitational energy that is released bythe transport of mass within the disk. Finally, we stress that future deeperALMA high-angular resolution observations are crucial to constrain thekinematic properties of high-z galaxies and to distinguish rotating disks fromkpc-scale mergers.