Key polynomials and minimal pairs

DOI10.1016/j.jalgebra.2018.12.022zbMath1498.13011arXiv1711.04296OpenAlexW2963167679WikidataQ128564282 ScholiaQ128564282MaRDI QIDQ1714847

Josnei Novacoski

Publication date: 1 February 2019

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

Full work available at URL: https://arxiv.org/abs/1711.04296

zbMATH Keywords

minimal pairskey polynomialslocal uniformization

Mathematics Subject Classification ID

Valuations and their generalizations for commutative rings (13A18) Valuation rings (13F30) Transcendental field extensions (12F20) General valuation theory for fields (12J20)

Related Items (22)

On the ranks and implicit constant fields of valuations induced by pseudo monotone sequences ⋮ Rigidity of valuative trees under Henselization ⋮ Limit key polynomials as \(p\)-polynomials ⋮ Valuation-transcendental extensions and pseudo-monotone sequences ⋮ Extensions of valuations to rational function fields over completions ⋮ Generating sequences and key polynomials ⋮ The defect formula ⋮ Graded rings associated to valuations and direct limits ⋮ Abstract key polynomials and distinguished pairs ⋮ MacLane-Vaquié chains and valuation-transcendental extensions ⋮ Valuations with an infinite limit-depth ⋮ A characterization for the defect of rank one valued field extensions ⋮ Minimal pairs, minimal fields and implicit constant fields ⋮ Minimal pairs, truncations and diskoids ⋮ On MacLane-Vaquié key polynomials ⋮ On common extensions of valued fields ⋮ Of limit key polynomials ⋮ Valuations on \(K[x\) approaching a fixed irreducible polynomial] ⋮ On truncations of valuations ⋮ Extensions of a valuation from $K$ to $K[x$] ⋮ On the implicit constant fields and key polynomials for valuation algebraic extensions ⋮ Abstract key polynomials and MacLane-Vaquié chains

Cites Work

• Unnamed Item
• A theorem of characterization of residual transcendental extensions of a valuation
• Abstract key polynomials and comparison theorems with the key polynomials of Mac Lane-Vaquié
• Minimal pairs of definition of a residual transcendental extension of a valuation
• Resolution of singularities of threefolds in positive characteristic. I: Reduction to local uniformization on Artin-Schreier and purely inseparable coverings
• Every place admits local uniformization in a finite extension of the function field
• Resolution of singularities of threefolds in positive characteristic. II
• Key polynomials and pseudo-convergent sequences
• Resolution of singularities of an algebraic variety over a field of characteristic zero. I
• Maximal fields with valuations. I, II
• Extension d’une valuation
• Value groups, residue fields, and bad places of rational function fields

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