The decline in ocean primary production is one of the most alarming consequences of anthropogenic climate change. This decline could indeed lead to a decrease in marine biomass and fish catch, as highlighted by recent policyrelevant reports. Because of computational constraints, current Earth system models used to project ocean primary production under global warming scenarios have to parameterize flows occurring below the resolution of their computational grid (typically 1°). To overcome these computational constraints, we use an ocean biogeochemical model in an idealized configuration representing a mid-latitude double-gyre circulation and perform global warming simulations under an increasing horizontal resolution (from 1 to 1/27°) and under a large range of parameter values for the eddy parameterization employed in the coarse-resolution configuration. In line with projections from Earth system models, all our simulations project a marked decline in net primary production in response to the global warming forcing. Whereas this decline is only weakly sensitive to the eddy parameters in the eddy-parameterized coarse 1 • resolution simulations, the simulated decline in primary production in the subpolar gyre is halved at the finest eddy-resolving resolution (−12 % at 1/27° vs. −26 % at 1°) at the end of the 70-yearlong global warming simulations. This difference stems from the high sensitivity of the sub-surface nutrient transport to model resolution. Although being only one piece of a much broader and more complicated response of the ocean to climate change, our results call for improved representation of the role of eddies in nutrient transport below the seasonal mixed layer to better constrain the future evolution of marine biomass and fish catch potential.