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Algebraic curves admitting the same Galois closure for two projections
A criterion for the existence of a plane model of an algebraic curve such that the Galois closures of projections from two points are the same is...
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Galois closures and elementary components of Hilbert schemes of points
Bhargava and the first-named author of this paper introduced a functorial Galois closure operation for finite-rank ring extensions, generalizing...
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Galois covers of singular curves in positive characteristics
We study the étale fundamental group of a singular reduced connected curve defined over an algebraically closed field of an arbitrary prime...
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Deformation of Rigid Conjugate Self-dual Galois Representations
In this article, we study deformations of conjugate self-dual Galois representations. The study is twofold. First, we prove an R=T type theorem for a...
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Preliminaries: Fundamental Groups and Galois Groups
The purpose of this chapter is to recollect the preliminary materials from topology and number theory, to aid the reader. In particular, we present a...
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Galois cohomology and profinitely solitary Chevalley groups
For every number field and every Cartan Killing type, there is an associated split simple algebraic group. We examine whether the corresponding...
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Infinite Galois Theory and Profinite Groups
The usual Galois correspondence between subgroups of Galois groups of finite Galois extensions and intermediate fields is not valid for infinite...
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Galois and the simple group of order 60
In his testamentary letter to Auguste Chevalier, Évariste Galois states that, in modern terminology, the smallest simple group has order 60. No proof...
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Galois Stratification over Finite Fields
Chapter 34 establishes the Galois stratification procedure over a fixed field K with elimination theory. The outcome is an explicit decision...
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Arithmetic statistics for Galois deformation rings
Given an elliptic curve E defined over the rational numbers and a prime p at which E has good reduction, we consider the Galois deformation ring...
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Symmetric Galois groups under specialization
Given an irreducible bivariate polynomial f ( t, x ) ∈ ℚ[ t, x ], what groups H appear as the Galois group of f ( t 0 , x ) for infinitely many t 0 ∈ ℚ? How...
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The Galois action on the lower central series of the fundamental group of the Fermat curve
Information about the absolute Galois group G K of a number field K is encoded in how it acts on the étale fundamental group π of a curve X defined...
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Galois Groups over Hilbertian Fields
Given a field K, one may ask which finite groups occur as Galois groups over K. If K is Hilbertian, then every finite group that occurs over K(t),...
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Galois Stratification
Chapter 34 extends the constructive field theory and algebraic geometry of Chapter 22, in contrast to Chapter 23, to give effective decision...
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Link Groups and Galois Groups with Restricted Ramification
As explained in Chap. 3 , our basic idea is to regard a Galois group with restricted ramification...
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On the outer automorphism groups of the absolute Galois groups of mixed-characteristic local fields
In the present paper, we study the outer automorphism groups of the absolute Galois groups of mixed-characteristic local fields from the point of...
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GALOIS AUTOMORPHISMS AND CLASSICAL GROUPS
In a previous work, the second-named author gave a complete description of the action of automorphisms on the ordinary irreducible characters of the...
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Chasing Maximal Pro-p Galois Groups via 1-Cyclotomicity
Let p be a prime. We prove that certain amalgamated free pro- p products of Demushkin groups with pro- p -cyclic amalgam cannot give rise to a...
