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Motivated by the recent observation of superconductivity in strontium dopedNdNiO$_2$, we study the superconducting instabilities in this system fromvarious vantage points. Starting with first-principles calculations, weconstruct two distinct tight-binding models, a simpler single-orbital as wellas a three-orbital model, both of which capture the key low energy degrees offreedom to varying degree of accuracy. We study superconductivity in bothmodels using the random phase approximation (RPA). We then analyze the problemat stronger coupling, and study the dominant pairing instability in theassociated t-J model limit. In all instances, the dominant pairing tendency isin the $d_{x^2-y^2}$ channel, analogous to the cuprate superconductors.

Robust $d_{x^2-y^2}$-wave superconductivity of infinite-layer nickelates