Search results for " Galois groups"

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A survey on algebraic dilatations

2023

In this text, we wish to provide the reader with a short guide to recent works on the theory of dilatations in Commutative Algebra and Algebraic Geometry. These works fall naturally into two categories: one emphasises foundational and theoretical aspects and the other applications to existing theories.

torsorsaffine modificationsdifferential Galois groupsformal blowupsNéron blowups[MATH] Mathematics [math]Commutative Algebra (math.AC)shtukasMathematics - Algebraic Geometryaffine blowupsFOS: Mathematicsalgebraic dilatations[MATH]Mathematics [math]Algebraic Geometry (math.AG)multi-centered dilatationsdilatations of schemesA 1 -homotopy theoryKaliman-Zaidenberg modificationslevel structuresMoy-Prasad isomorphismrepresentations of p-adic groupsMathematics - Commutative Algebramono-centered dilatationslocalizations of ringscongruent isomorphismsTannakian groupsaffine geometry
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MR 3215343 Reviewed Pirola G.P., Rizzi C. and Schlesinger E. A new curve algebraically but not rationally uniformized by radicals. Asian J. Math., 18…

2014

A smooth projective complex curve C is called rationally uniformized by radicals if there exists a covering map C \rightarrow P^1 with solvable Galois group. C is called algebraically uniformized by radicals if there exists a finite covering C^{\prime} \rightarrow C with C^{\prime} rationally uniformized by radicals. Abramovich and Harris posed the following problem in [D. Abramovich and J. Harris, Abelian varieties and curves in $W_{d}(C)$, Compositio Math., 78 (1991), pp. 227–-238]. \vspace{1ex} Statement S(d, h, g): \textit{Suppose C^{\prime} \rightarrow C is a nonconstant map of smooth curves with C of genus g. If C^{\prime} admits a map of degree d or less to a curve of genus h or less…

Monodromy groups Galois groups projective curves.Settore MAT/03 - Geometria
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