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Analyses of type Ia supernovae (SNe Ia) have found puzzling correlationsbetween their standardised luminosities and host galaxy properties: SNe Ia inhigh-mass, passive hosts appear brighter than those in lower-mass, star-forminghosts. We examine the host galaxies of SNe Ia in the Dark Energy Surveythree-year spectroscopically-confirmed cosmological sample, obtainingphotometry in a series of "local" apertures centred on the SN, and for theglobal host galaxy. We study the differences in these host galaxy properties,such as stellar mass and rest-frame $U-R$ colours, and their correlations withSN Ia parameters including Hubble residuals. We find all Hubble residual stepsto be $>3\sigma$ in significance, both for splitting at the traditionalenvironmental property sample median and for the step of maximum significance.For stellar mass, we find a maximal local step of $0.098\pm0.018$ mag; $\sim0.03$ mag greater than the largest global stellar mass step in our sample($0.070 \pm 0.017$ mag). When splitting at the sample median, differencesbetween local and global $U-R$ steps are small, both $\sim 0.08$ mag, but aremore significant than the global stellar mass step ($0.057\pm0.017$ mag). Wesplit the data into sub-samples based on SN Ia light curve parameters: stretch($x_1$) and colour ($c$), finding that redder objects ($c > 0$) have largerHubble residual steps, for both stellar mass and $U-R$, for both local andglobal measurements, of $\sim0.14$ mag. Additionally, the bluer (star-forming)local environments host a more homogeneous SN Ia sample, with local $U-R$r.m.s. scatter as low as $0.084 \pm 0.017$ mag for blue ($c < 0$) SNe Ia inlocally blue $U-R$ environments.

The Effect of Environment on Type Ia Supernovae in the Dark Energy Survey Three-Year Cosmological Sample