A note on principal ideals and smooth curves

DOI10.1016/0021-8693(82)90009-6zbMath0507.14023OpenAlexW2085118793MaRDI QIDQ1837255

Michael D. Fried

Publication date: 1982

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(82)90009-6

zbMATH Keywords

principal idealPicard varietyMordell conjecturecoordinate ring of affine curve

Mathematics Subject Classification ID

Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) (14M05) Ideals and multiplicative ideal theory in commutative rings (13A15) Singularities of curves, local rings (14H20) Picard groups (14C22)

Related Items (2)

Set-theoretic complete intersection points on curves ⋮ Affine curves on which every point is a set-theoretic complete intersection

Cites Work

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• Principal ideals and smooth curves
• On Hilbert's irreducibility theorem
• Solving diophantine problems over all residue class fields of a number field and all finite fields
• Poncelet correspondences: finite correspondences; Ritt's theorem; and the Griffiths-Harris configuration for quadrics
• Galois Cohomology
• On the equations defining Abelian varieties. I-III
• Abelian varieties over \(p\)-adic ground fields
• Fields of definition of function fields and hurwitz families — groups as galois groups
• Constructive normalization of an algebraic variety
• Lectures on Curves on an Algebraic Surface. (AM-59)
• Further Pathologies in Algebraic Geometry
• The Jacobian Variety of an Algebraic Curve
• On a Theorem of Torelli

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