[en] We have developed a new coherent dedispersion mode to study the emission of fast radio bursts (FRBs) that trigger the voltage capture capability of the Australian SKA Pathfinder (ASKAP) interferometer. In principle the mode can probe emission timescales down to 3 ns with full polarimetric information preserved. Enabled by the new capability, here we present a spectropolarimetric analysis of FRB 181112 detected by ASKAP, localized to a galaxy at redshift 0.47. At microsecond time resolution the burst is resolved into four narrow pulses with a rise time of just 15 μs for the brightest. The pulses have a diversity of morphology, but do not show evidence for temporal broadening by turbulent plasma along the line of sight, nor is there any evidence for periodicity in their arrival times. The pulses are highly polarized (up to 95%), with the polarization position angle varying both between and within pulses. The pulses have apparent rotation measures that vary by $15\pm <!--\; ??\; -->2\mathrm{r}\mathrm{a}\mathrm{d}{\mathrm{m}}^{-<!--\; ???\; -->2}$ and apparent dispersion measures that vary by $0.041\pm <!--\; ??\; -->0.004\mathrm{p}\mathrm{c}{\mathrm{c}\mathrm{m}}^{-<!--\; ???\; -->3}$. Conversion between linear and circular polarization is observed across the brightest pulse. We conclude that the FRB 181112 pulses are most consistent with being a direct manifestation of the emission process or the result of propagation through a relativistic plasma close to the source. This demonstrates that our method, which facilitates high-time-resolution polarimetric observations of FRBs, can be used to study not only burst emission processes, but also a diversity of propagation effects present on the gigaparsec paths they traverse.