On the nilpotent functions at a non-degenerate arc

DOI10.1007/s00229-020-01209-yzbMath1458.14020OpenAlexW2970202739MaRDI QIDQ2663060

Mercedes Haiech, David Bourqui

Publication date: 15 April 2021

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00229-020-01209-y

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Singularities in algebraic geometry (14B05) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Derivations and commutative rings (13N15) Ideals and multiplicative ideal theory in commutative rings (13A15) Differential algebra (12H05) Completion of commutative rings (13B35) Arcs and motivic integration (14E18) Formal neighborhoods in algebraic geometry (14B20)

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Cites Work

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• A remark on Berger's conjecture, Kolchin's theorem, and arc schemes
• The Krull intersection theorem
• The Nash problem on arc families of singularities
• Versal deformations of formal arcs
• On torsion Kähler differential forms
• Motivic integration
• The arc space of a toric variety
• Differentials on the arc space
• Kolchin's irreducibility theorem.
• A curve selection lemma in spaces of arcs and the image of the Nash map
• Towards the singular locus of the space of arcs
• The Drinfeld-Grinberg-Kazhdan Theorem for formal schemes and singularity theory
• The minimal formal models of curve singularities
• Arc Schemes in Geometry and Differential Algebra
• The Grinberg–Kazhdan Formal Arc Theorem and the Newton Groupoids
• THE DRINFELD–GRINBERG–KAZHDAN THEOREM IS FALSE FOR SINGULAR ARCS
• Greenberg Approximation and the Geometry of Arc Spaces

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