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  "body": "\n## Summary\n\nThe Picard group of a ringed space $X$ is the group of isomorphism classes of invertible sheaves on $X$.\nIts group law is the tensor product.\nIt is a basic invariant of a scheme, and it measures the line bundles available for maps to projective space.\nFor the spectrum of a Dedekind domain it is the ideal class group.\nFor projective space $\\mathbb{P}^n$ over a field, with $n \\ge 1$, it is $\\Z$, generated by $\\mathcal{O}(1)$.\n\n## Explanations\n\n### L1 human\n\nLine bundles can be multiplied by the tensor product, and each line bundle has an inverse, its dual.\nSo the line bundles on a space, up to isomorphism, form a group: the Picard group.\nOn affine space every line bundle is trivial, so the Picard group is trivial.\nOn projective space every line bundle is a power of one basic bundle, so the Picard group is the integers.\n",
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