Resolution of singularities and modular Galois theory

DOI10.1090/S0273-0979-00-00892-2zbMath0999.12003OpenAlexW1966667920MaRDI QIDQ2706625

Shreeram S. Abhyankar

Publication date: 20 March 2001

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0273-0979-00-00892-2

zbMATH Keywords

Galois groupresolution of singularitiesfundamental groupsGalois theoryautobiography

Mathematics Subject Classification ID

Separable extensions, Galois theory (12F10) Extensions, wreath products, and other compositions of groups (20E22) Coverings of curves, fundamental group (14H30) Simple groups: alternating groups and groups of Lie type (20D06)

Related Items (16)

Proximity relations for real rank one valuations dominating a local regular ring ⋮ Ramification of valuations ⋮ On the inertia conjecture for alternating group covers ⋮ Explicit Drinfeld moduli schemes and Abhyankar's generalized iteration conjecture ⋮ Abhyankar's affine arithmetic conjecture for the symmetric and alternating groups ⋮ Towards the generalized purely wild inertia conjecture for product of alternating and symmetric groups ⋮ On the inertia conjecture and its generalizations ⋮ On vectorial polynomials and coverings in characteristic 3 ⋮ Extensions with Galois group \(2^+S_4*D_8\) in characteristic 3 ⋮ Galois groups over function fields of positive characteristic ⋮ Resolution of singularities of threefolds in positive characteristic. I: Reduction to local uniformization on Artin-Schreier and purely inseparable coverings ⋮ Alternating group covers of the affine line ⋮ 2𝑆₄*𝑄₈-extensions in characteristic 3 ⋮ Abhyankar’s conjectures in Galois theory: Current status and future directions ⋮ Polynomials with AGL-monodromy ⋮ Local monomialization of transcendental extensions.

Cites Work

• Determinantal loci and the flag variety
• Schur covers and Carlitz's conjecture
• Braid group action via \(\text{GL}_ n(q)\) and \(\text{U}_ n(q)\), and Galois realizations
• 2-transitive and antiflag transitive collineation groups of finite projective spaces
• On the maximal subgroups of the finite classical groups
• Some finite groups which appear as Gal L/K, where \(K\subseteq {\mathbb{Q}}(\mu _ n)\)
• Homogeneous designs and geometric lattices
• \(\mathrm{GL}_n (q)\) as Galois group over the rationals
• Transitive linear groups and linear groups which contain irreducible subgroups of prime order. II
• Local uniformization on algebraic surfaces over ground fields of characteristic \(p\neq 0\)
• Weighted expansions for canonical desingularization. With foreword by U. Orbanz
• Coinsertion and standard bitableaux
• On Hilbert polynomial of certain determinantal ideals
• Generalized roinsertive correspondence between multitableaux and multimonomials
• Generalized rodeletive correspondence between multitableaux and multimonomials
• Young tableaux and linear independence of standard monomials in multiminors of a multimatrix
• Combinatorial meaning of the coefficients of a Hilbert polynomial
• Generalized coinsertion and standard multitableaux
• Mathieu-group coverings of the affine line
• Transitive linear groups and linear groups which contain irreducible subgroups of prime order
• Buildings of spherical type and finite BN-pairs
• On Hilbert's irreducibility theorem
• Rank 3 characterizations of classical geometries
• Alternating group coverings of the affine line for characteristic greater than two
• Coverings of the affine line in characteristic \(p>0\) and Abhyankar's conjecture
• Abhyankar's conjecture on Galois groups over curves
• Alternating group coverings of the affine line for characteristic two
• Nice equations for nice groups
• Local weak simultaneous resolution for high rational ranks
• Local factorization of birational maps
• Bijection between indexed monomials and standard bitableaux
• Kennzeichnung endlicher linearer Gruppen als Permutationsgruppen
• On the foundations of polar geometry
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Séconde partie)
• An algorithm on polynomials in one indeterminate with coefficients in a two dimensional regular local domain
• Galois properties of points of finite order of elliptic curves
• Resolution of singularities of an algebraic variety over a field of characteristic zero. I
• On Hilbertian ideals
• The reduction of the singularities of an algebraic surface
• On the theory of local rings
• Reduction of the singularities of algebraic three dimensional varieties
• Monoidal Transforms of Regular Local Rings
• Resolvents Of Certain Linear Groups In a Finite Field
• Algebraic Groups Over Finite Fields
• Simultaneous Resolution for Algebraic Surfaces
• On the Valuations Centered in a Local Domain
• Coverings of Algebraic Curves
• Tame Coverings and Fundamental Groups of Algebraic Varieties: Part I: Branch Loci with Normal Crossings; Applications: Theorems of Zariski and Picard
• Classifying the finite simple groups
• The Affine Permutation Groups of Rank Three
• Finite Permutation Groups and Finite Simple Groups
• Galois theory on the line in nonzero characteristic
• Explicit Class Field Theory for Rational Function Fields
• Historical Ramblings in Algebraic Geometry and Related Algebra
• Semilinear transformations
• A Class of Exceptional Polynomials
• Some More Mathieu Group Coverings in Characteristic Two
• Local fundamental groups of algebraic varieties
• Projective polynomials
• Galois theory of Moore-Carlitz-Drinfeld modules
• Polynomial expansion
• Once more nice equations for nice groups
• Characterization of classical groups by orbit sizes on the natural module
• Again nice equations for nice groups
• More nice equations for nice groups
• Small Mathieu Group Coverings in Characteristic Two
• Further Nice Equations for Nice Groups
• Bivariate factorizations connecting Dickson polynomials and Galois theory
• Theory and applications of holomorphic functions on algebraic varieties over arbitrary ground fields
• Foundations of a General Theory of Birational Correspondences
• On the Ramification of Algebraic Functions
• On a class of doubly transitive permutation groups
• On a class of doubly transitive groups
• On the subgroup structure of classical groups
• Galois groups of generalized iterates of generic vectorial polynomials.
• Descent principle in modular Galois theory
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