Key polynomials and pseudo-convergent sequences

DOI10.1016/j.jalgebra.2017.11.006zbMath1391.13009arXiv1611.05679OpenAlexW2963285270MaRDI QIDQ1682073

Mark Spivakovsky, Josnei Novacoski

Publication date: 28 November 2017

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

Full work available at URL: https://arxiv.org/abs/1611.05679

zbMATH Keywords

valuationskey polynomialspseudo-convergent sequences

Mathematics Subject Classification ID

Valuations and their generalizations for commutative rings (13A18)

Related Items (26)

On the ranks and implicit constant fields of valuations induced by pseudo monotone sequences ⋮ 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 ⋮ Graded rings associated to valuations and direct limits ⋮ Erratic birational behavior of mappings in positive characteristic ⋮ Abstract key polynomials and distinguished pairs ⋮ MacLane-Vaquié chains and valuation-transcendental extensions ⋮ A characterization for the defect of rank one valued field extensions ⋮ Key polynomials and minimal pairs ⋮ Generating sequences and semigroups of valuations on 2-dimensional normal local rings ⋮ Minimal pairs, minimal fields and implicit constant fields ⋮ Extensions of valuations to the Henselization and completion ⋮ Minimal pairs, truncations and diskoids ⋮ On MacLane-Vaquié key polynomials ⋮ On common extensions of valued fields ⋮ Of limit key polynomials ⋮ Discrete equivalence of non-positive at infinity plane valuations ⋮ Valuations on \(K[x\) approaching a fixed irreducible polynomial] ⋮ On truncations of valuations ⋮ Extensions of valuations to the Henselization and completion of a local ring ⋮ Extensions of a valuation from $K$ to $K[x$] ⋮ Resolution of Singularities: An Introduction ⋮ On the implicit constant fields and key polynomials for valuation algebraic extensions ⋮ Abstract key polynomials and MacLane-Vaquié chains

Cites Work

• Unnamed Item
• Abstract key polynomials and comparison theorems with the key polynomials of Mac Lane-Vaquié
• Every place admits local uniformization in a finite extension of the function field
• Key polynomials
• Maximal fields with valuations. I, II
• Valuations in Function Fields of Surfaces
• Extension d’une valuation

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