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  "body": "\n## Summary\n\nA smooth morphism of schemes is a flat morphism, locally of finite presentation, whose fibres are smooth schemes over their residue fields.\nIt is the algebraic analogue of a submersion of differentiable manifolds.\nA variety over a field is smooth exactly when its structure morphism is smooth, and smooth morphisms are stable under composition and base change.\n\n## Explanations\n\n### L1 human\n\nA smooth morphism is a family of smooth spaces that fit together without jumps.\nNear each point, it looks like the projection of a product of the target with an affine space, up to an étale change of coordinates.\nThe projection $\\mathbb{A}^2 \\to \\mathbb{A}^1$ is smooth: each fibre is a line.\nThe map from the curve $y^2 = x^2(x + 1)$ to a point is not smooth, because the curve has a node at the origin.\n",
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