Resolution of singularities of threefolds in positive characteristic. I: Reduction to local uniformization on Artin-Schreier and purely inseparable coverings

From MaRDI portal
Publication:949586

DOI10.1016/j.jalgebra.2008.03.032zbMath1159.14009OpenAlexW160482058WikidataQ57601952 ScholiaQ57601952MaRDI QIDQ949586

Olivier Piltant, Vincent Cossart

Publication date: 21 October 2008

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2008.03.032




Related Items (73)

Rational curves on del Pezzo surfaces in positive characteristicReduced Steenrod operations and resolution of singularitiesInseparable local uniformizationThree dimensional canonical singularities in codimension two in positive characteristicThe X-method for klt surfaces in positive characteristicSlope inequality for families of curves over surfacesCanonical singularities of dimension three in characteristic \(2\) which do not follow Reid's rulesOn the universal \(\mathrm {CH}_0\) group of cubic threefolds in positive characteristicA simpler proof of toroidalization of morphisms from 3-folds to surfacesResolution of singularities of arithmetical threefoldsThe \(\tau \)-invariant and eliminationLog canonical thresholds of del Pezzo surfaces in characteristic \(p\)Resolutions in local algebra and singularity theory. Abstracts from the workshop held February 5--11, 2023An axiomatic version of Zariski's patching theoremThe Grothendieck–Serre conjecture over valuation ringsFormal prime ideals of infinite value and their algebraic resolutionMonomial valuations, cusp singularities, and continued fractionsTechniques for the study of singularities with applications to resolution of 2-dimensional schemesEffective bounds of linear series on algebraic varieties and arithmetic varietiesFirst order deformations of schemes with normal crossing singularitiesAbundance for non‐uniruled 3‐folds with non‐trivial Albanese maps in positive characteristicsKey polynomials and minimal pairsAbundance for 3-folds with non-trivial Albanese maps in positive characteristicCycles of singularities appearing in the resolution problem in positive characteristic\(F\)-rationality of Rees algebrasOn the problem of resolution of singularities: its development and current status (from a myopic point of view of one researcher struggling with the problem)Equivariant minimal model programLocal monomialization of analytic mapsPartial local resolution by characteristic zero methodsTopology of spaces of valuations and geometry of singularitiesA note on Iitaka's conjecture \(C_{3,1}\) in positive characteristicsPerron TransformsEquimultiplicity, algebraic elimination, and blowing-upExistence of Mori fibre spaces for 3-folds in char \(p\)Characteristic polyhedra of singularities without completionRamification of Valuations and Local Rings in Positive CharacteristicSingularities in positive characteristic, stratification and simplification of the singular locusWeights in arithmetic geometryMinimal pairs, truncations and diskoidsToward resolution of singularities over a field of positive characteristic (The idealistic filtration program). II: Basic invariants associated to the idealistic filtration and their propertiesRational points on log Fano threefolds over a finite fieldCharacterizing the increase of the residual order under blowup in positive characteristicElimination of ramification. II: Henselian rationalityRelative dynamical degrees of correspondences over a field of arbitrary characteristicFinite morphisms and Nash multiplicity sequencesOn the simplication of singularities by blowing up at equimultiple centersCharacteristic polyhedra of singularities without completion. IIResolution of singularities of threefolds in mixed characteristic: case of small multiplicityOn quasi-purity of the branch locusContact loci and Hironaka's orderSubadditivity of Kodaira dimension does not hold in positive characteristicGENERAL HYPERPLANE SECTIONS OF THREEFOLDS IN POSITIVE CHARACTERISTICResolution of singularities of threefolds in positive characteristic. IITruncated local uniformization of formal integrable differential formsOn the abundance problem for 3-folds in characteristic \(p>5\)Murthy's conjecture on 0-cyclesPositive characteristic algebraic geometryEmbedded desingularization for arithmetic surfaces – toward a parallel implementationBook Review: Resolution of singularities; Lectures on resolution of singularitiesSubadditivity of Kodaira dimensions for fibrations of three-folds in positive characteristicsContinuity of plurisubharmonic envelopes in non-Archimedean geometry and test ideals. With an appendix by José Ignacio Burgos Gil and Martín Sombra.On the three dimensional minimal model program in positive characteristicDefect and local uniformizationOn the problem of resolution of singularities in positive characteristic (Or: A proof we are still waiting for)Monoidal transforms and invariants of singularities in positive characteristicResolution of Singularities: An IntroductionUnramified Brauer groups of conic bundle threefolds in characteristic twoON THE BASE-POINT-FREE THEOREM OF 3-FOLDS IN POSITIVE CHARACTERISTICOn rational connectedness of globally \(F\)-regular threefoldsDiophantine problems over tamely ramified fieldsOn the homeomorphism type of some spaces of valuationsMultiplicity along points of a radicial covering of a regular varietyCounterexamples to local monomialization in positive characteristic



Cites Work


This page was built for publication: Resolution of singularities of threefolds in positive characteristic. I: Reduction to local uniformization on Artin-Schreier and purely inseparable coverings