Picard groups of singular affine curves over a perfect field
Let R be the coordinate ring of an irreducible affine curve over a perfect field k, and let S be the normalization. It is shown that the canonical map Pic(R)\(\to Pic(S)\) is an isomorphism if (and only if) its kernel is a finitely generated abelian group. Moreover, these conditions hold if and only if the curve has at most one singularity and its local ring is analytically isomorphic to a restricted power series ring \(F+XKX\), for suitable finite algebraic extensions \(K\supseteq F\supseteq k\).
coordinate ring of an irreducible affine curve
scientific article; zbMATH DE number 4037981
scientific article