A generalisation of the Abhyankar Jung theorem to associated graded rings of valuations

DOI10.1017/S0305004115000687zbMath1371.13028arXiv1411.4843OpenAlexW2962719717MaRDI QIDQ5360370

Steven Dale Cutkosky

Publication date: 28 September 2017

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.4843

Mathematics Subject Classification ID

Valuations and their generalizations for commutative rings (13A18) Valuation rings (13F30) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30)

Related Items

The role of defect and splitting in finite generation of extensions of associated graded rings along a valuation ⋮ Extensions of valuations to the Henselization and completion of a local ring

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Ramification of valuations
• A classification of Artin-Schreier defect extensions and characterizations of defectless fields
• A new proof of the Jung-Abhyankar theorem
• Toroidalization of generating sequences in dimension two function fields
• Toroidalization of generating sequences in dimension two function fields of positive characteristic
• Local uniformization on algebraic surfaces over ground fields of characteristic \(p\neq 0\)
• Extensions of valuations to the completion of a local domain
• The Abhyankar-Jung theorem
• Equimultiplicity, algebraic elimination, and blowing-up
• The tame fundamental groups of a formal neighbourhood of a divisor with normal crossings on a scheme
• Extending a valuation centred in a local domain to the formal completion
• Valuations in Function Fields of Surfaces
• On the Valuations Centered in a Local Domain
• Ramification Theoretic Methods in Algebraic Geometry (AM-43)
• Polytopes, Rings, and K-Theory
• Overweight deformations of affine toric varieties and local uniformization
• Valuation semigroups of two‐dimensional local rings
• Ramification of Valuations and Local Rings in Positive Characteristic
• On the Ramification of Algebraic Functions