# Questions tagged [galois-theory]

Galois theory, named after Évariste Galois, provides a connection between field theory and group theory. Using Galois theory, certain problems in field theory can be reduced to group theory, which is, in some sense, simpler and better understood.

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### $p$-adic Hodge theoretic properties of global Galois representations via $\ell$-Frobenii

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### Reducibility of a cubic over a number field

**3**

**1**answer

### Centralizer of the absolute Galois group of a number field

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### A quantity associated to a field extension

**4**

**1**answer

### Can every square root be represented as a linear combination on roots of unity? [duplicate]

**1**

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### Effective Hilbert's Irreducibility Theorem and Irreducibility of $f(x)+1$, $f(x)\in\mathbb{Q}[x]$ reducible

**4**

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### perfect fields in positive characteristic

**3**

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### Dedekind Zeta functions of Biquadratic fields

**9**

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### An explicit isomorphism $K^\times/K^{\times p} \cong K^\flat/\wp K^\flat$ where $K \supset \mu_p$ is perfectoid field of mixed characteristic $(0, p)$

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### Is $\operatorname{Aut}(\mathcal{M})$ a fundamental group in Grothendieck's sense?

**2**

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### Field whose absolute Galois group is $\mathbb{Z}_p$

**3**

**1**answer

### Connecting different ways of constructing cubic extensions of $\mathbb{Q}$

**1**

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### Conjecture about arcsin and $\sqrt{\quad}$

**1**

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### Are absolute Galois groups condensed?

**9**

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### What is the indecomposable decomposition of holomorphic differentials of an Artin-Schreier curve C as a Z/p-representation?

**2**

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### Permutation group with a nice lattice of block systems

**4**

**1**answer

### How hard is it to find the first layer of this basic $\mathbb{Z}_p$-extension?

**4**

**1**answer

### References for Hopf Galois module theory

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### Compass and straightedge construction of Poncelet polygons

**10**

**1**answer

### Origin and context of adjunctions inducing equivalences between full subcategories

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### Motivic Galois correspondence

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### Classifying twists for a general moduli problem

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**1**answer

### Upper bound for discriminant of Galois closure

**2**

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### Finitely generated subgroups of the absolute Galois group

**5**

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### Do algebraic completion/topological completion of fields always terminate? If so, are they unique?

**1**

**3**answers

### What are the main open problems in Group Theory and Galois Theory? [closed]

**1**

**1**answer

### Galois group acts by the $i$-th power of the Teichmuller character on $H$

**10**

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### Representing finite sums of rational powers of 2

**6**

**1**answer

### What is the Galois group of one ultrapower over another ultrapower?

**1**

**1**answer

### When is a infinite transcendence-degree rigid fields fixed by a finite extension?

**5**

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### Finite groups arising as Galois groups of maximal unramified extension of number fields

**7**

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### Counter example of a radical extension that is not Galois/normal over $\mathbb{Q}(\omega)$?

**1**

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### What is known about the algebraic completion of a monoid?

**7**

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### Possible Galois groups of residue fields of ramification points of a Galois branched cover of curves

**3**

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### Can you define the absolute Galois groupoid in von Neumann–Bernays–Gödel set theory?

**1**

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### Is this an explicit construction of a Hurwitz space with Galois group Z/p, p distinct branch points, and inertia group Z/(p-1)?

**5**

**1**answer

### Inverse Galois problem for non-Galois extensions

**3**

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### Galois theory of periods of algebraic varieties PhD project

**2**

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### Linear relation between polynomial roots

**1**

**3**answers

### Minimal polynomial in $\mathbb Z[x]$ of seventh degree with given roots

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### Galois groups associated to matrices

**1**

**1**answer

### Galois extensions of ring spectra and subextensions

**3**

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### Infinite separable extensions

**3**

**1**answer

### Field of definition/moduli through the monodromy

**1**

**1**answer

### Reference book for Galois extension [closed]

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### Etale cohomology and Kummer theory

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### Doubt regarding invariance of discrete absolute value under automorphism

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### Concerning the Galois resolvent

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### Polynomials for the alternating group $A_n$

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