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Persistent disparities in academic achievement between students from high- and low-poverty neighborhoods are widely attributed to differences in school quality. Using nationally representative data from over 18,000 students and nearly 1,000 elementary schools, we examine how the schools serving students from different neighborhoods vary across more than 170 characteristics, including detailed measures of their composition, resources, curriculum, instructional practices, academic climate, and effectiveness. Our findings document significant differences in demographic composition between schools serving high- and low-poverty neighborhoods, but comparatively little variation in other dimensions of the school environment. With novel machine learning methods tailored for high-dimensional data, we estimate that equalizing all these different factors would reduce the achievement gap by less than 10\%, primarily through changes in school composition. These results suggest that the primary drivers of place-based disparities in achievement lie outside of elementary schools, underscoring the need to address broader structural inequalities as part of any effort to reduce achievement gaps.