Field
Commutative Algebra
The theory of commutative rings and their ideals, and the algebraic ground on which algebraic geometry is built.
Publications in Commutative Algebra
Browse academic publications and research works in this field
A complete local ring with a finitely generated maximal ideal is Noetherian. Drop completeness and it fails: an ultraproduct construction gives a non-Noetherian local ring whose maximal ideal is principal.
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Every finite flat commutative group scheme over a noetherian local ring is the torsion component of the Picard scheme of a smooth projective scheme with 3-dimensional fibers, built as a quotient of a complete intersection. An application: Hodge numbers that jump in a smooth projective family.
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