  Galaxy morphology is shaped by stellar activity, feedback, gas and dust
properties, and interactions with surroundings, and can therefore provide
insight into these processes. In this paper, we study the spatial offsets
between stellar and interstellar medium emission in a sample of 54
main-sequence star-forming galaxies at $z\sim4-6$ observed with the Atacama
Large Millimeter/submillimeter Array (ALMA) and drawn from the ALMA Large
Program to INvestigate C$^+$ at Early times (ALPINE). We find no significant
spatial offset for the majority ($\sim$ 70 percent) of galaxies in the sample
among any combination of [C II], far-infrared continuum, optical, and
ultraviolet emission. However, a fraction of the sample ($\sim$ 30 percent)
shows offsets larger than the median by more than 3$\sigma$ significance
(compared to the uncertainty on the offsets), especially between [C II] and
ultraviolet emission. We find that these significant offsets are of the order
of $\sim$0.5-0.7 arcsec, corresponding to $\sim$3.5-4.5 kiloparsecs. The
offsets could be caused by a complex dust geometry, strong feedback from stars
and active galactic nuclei, large-scale gas inflow and outflow, or a
combination of these phenomena. However, our current analysis does not
definitively constrain the origin. Future, higher resolution ALMA and JWST
observations may help resolve the ambiguity. Regardless, since there exist at
least some galaxies that display such large offsets, galaxy models and spectral
energy distribution fitting codes cannot assume co-spatial emission in all
main-sequence galaxies, and must take into account that the observed emission
across wavelengths may be spatially segregated.
