Ramification of valuations

DOI10.1016/S0001-8708(03)00082-3zbMath1105.14015OpenAlexW1976039770MaRDI QIDQ597135

Steven Dale Cutkosky, Olivier Piltant

Publication date: 6 August 2004

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0001-8708(03)00082-3

zbMATH Keywords

resolution of singularitiescharacteristic \(p\)

Mathematics Subject Classification ID

Global theory and resolution of singularities (algebro-geometric aspects) (14E15) Rational and birational maps (14E05) Valuations and their generalizations for commutative rings (13A18) Ramification problems in algebraic geometry (14E22)

Related Items

The valuation theory of deeply ramified fields and its connection with defect extensions ⋮ Monomialization of strongly prepared morphisms from nonsingular \(n\)-folds to surfaces ⋮ Essential finite generation of valuation rings in characteristic zero algebraic function fields ⋮ Constructing examples of semigroups of valuations ⋮ Semigroups of valuations on local rings ⋮ Counting the number of distinct distances of elements in valued field extensions ⋮ Value groups, residue fields, and bad places of rational function fields ⋮ Toroidalization of generating sequences in dimension two function fields ⋮ The role of defect and splitting in finite generation of extensions of associated graded rings along a valuation ⋮ Toroidalization of generating sequences in dimension two function fields of positive characteristic ⋮ Distances of elements in valued field extensions ⋮ Essentially finite generation of valuation rings in terms of classical invariants ⋮ Dependent Artin-Schreier defect extensions and strong monomialization ⋮ Erratic birational behavior of mappings in positive characteristic ⋮ A generalisation of the Abhyankar Jung theorem to associated graded rings of valuations ⋮ On the Jung method in positive characteristic. ⋮ A classification of Artin-Schreier defect extensions and characterizations of defectless fields ⋮ Resolution of singularities of threefolds in positive characteristic. I: Reduction to local uniformization on Artin-Schreier and purely inseparable coverings ⋮ Semiglobal models of extensions of two-dimensional local fields ⋮ Ramification of local rings along valuations ⋮ Ramification of Valuations and Local Rings in Positive Characteristic ⋮ Extensions of valuations to the Henselization and completion of a local ring ⋮ Selected methods for the classification of cuts, and their applications ⋮ Correction and notes to the paper ``A classification of Artin-Schreier defect extensions and characterizations of defectless fields ⋮ Ramification of higher local fields, approaches and questions ⋮ Local monomialization of transcendental extensions. ⋮ Defect and local uniformization ⋮ Local uniformization of Abhyankar valuations ⋮ Counterexamples to local monomialization in positive characteristic

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