Looking at ocean depth/latitude profiles of dissolved oxygen and nitrate. Why is dissolved oxygen low when nitrate is high?
In general the relationship between dissolved oxygen and nitrate is complex. While in areas of water mass formation, especially in the Arctic and Antarctic Oceans, nutrient concentration and dissolved oxygen can be high, water mass evolution and biological activity can rapidly modified these concentration. The relationship is affected by several factors including: 1) the age of the water mass: the "older" the water mass (longer time since in equilibrium with atmospheric oxygen), the lower the dissolved oxygen concentration; and 2) the proximity to primary productive areas like the surface: the higher the primary production, the lower the nitrate concentration.

In some parts of the interior of the Atlantic Ocean, the water masses present (North Atlantic Deep Water, Antarctic Bottom Water) are pretty old and haven't been in contact with the surface layers for a while, so their oxygen concentration is high while they remain nutrient rich. The water masses in the surface layers have recently been in contact with the atmosphere and thus have a high oxygen concentration. Meanwhile, by being near the surface they are subject to primary production that tends to rapidly consume the nutrients (like nitrate). The relationship is highly variable spatially specially near the coastal regions, where processes like upwelling/downwelling can rapidly modified nutrient and oxygen concentrations.