Extensions of valuations to the Henselization and completion

DOI10.1007/s40306-018-0267-yzbMath1427.14008arXiv1712.08562OpenAlexW2962835928MaRDI QIDQ2000799

Steven Dale Cutkosky

Publication date: 28 June 2019

Published in: Acta Mathematica Vietnamica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.08562

zbMATH Keywords

algebraically closed fieldcompletionlocal ringvaluationHenselizationring domination

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) Valuations and their generalizations for commutative rings (13A18) Morphisms of commutative rings (13B10) Valuation rings (13F30) Ramification and extension theory (11S15)

Related Items (2)

Some Ideas in Need of Clarification in Resolution of Singularities and the Geometry of Discriminants ⋮ Extensions of valuations to the Henselization and completion of a local ring

Cites Work

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• A construction for a class of valuations of the field \(k(X_1,\cdots ,X_d,Y)\) with large value group
• Local uniformization on algebraic surfaces over ground fields of characteristic \(p\neq 0\)
• Extensions of valuations to the completion of a local domain
• Key polynomials and pseudo-convergent sequences
• The role of defect and splitting in finite generation of extensions of associated graded rings along a valuation
• Formal prime ideals of infinite value and their algebraic resolution
• Constructing examples of semigroups of valuations
• Extending a valuation centred in a local domain to the formal completion
• Valuations in Function Fields of Surfaces
• Ramification Theoretic Methods in Algebraic Geometry (AM-43)
• Overweight deformations of affine toric varieties and local uniformization
• Valuation semigroups of two‐dimensional local rings
• Perron Transforms

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