Picard groups of singular affine curves over a perfect field
type: Item
instance of: scholarly article
title: Picard groups of singular affine curves over a perfect field
zbMATH Open document ID: 0637.14006
DOI: 10.1007/BF01215648
author: Roger Wiegand
published in: Mathematische Zeitschrift
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174010
review text: 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 \(K\supseteq F\supseteq k\).
Mathematics Subject Classification ID: 14C22
Mathematics Subject Classification ID: 14H20
zbMATH DE Number: 4037981
zbMATH Keywords: coordinate ring of an irreducible affine curve
zbMATH Keywords: Pic
zbMATH Keywords: Picard group
MaRDI profile type: Publication
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OpenAlex ID: W1995814366
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description: scientific article; zbMATH DE number 4037981