# 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.

**133**

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### Grothendieck-Teichmuller conjecture

**96**

**10**answers

### "Understanding" $\mathrm{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})$

**86**

**2**answers

### Is it possible to express $\int\sqrt{x+\sqrt{x+\sqrt{x+1}}}dx$ in elementary functions?

**75**

**8**answers

### The inverse Galois problem, what is it good for?

**71**

**2**answers

### The inverse Galois problem and the Monster

**71**

**2**answers

### Why is differential Galois theory not widely used?

**62**

**9**answers

### Galois Groups vs. Fundamental Groups

**61**

**3**answers

### Forcing as a new chapter of Galois Theory?

**58**

**4**answers

### Degree of sum of algebraic numbers

**50**

**9**answers

### Is Galois theory necessary (in a basic graduate algebra course)?

**50**

**2**answers

### Does one real radical root imply they all are?

**46**

**1**answer

### Which small finite simple groups are not yet known to be Galois groups over Q?

**44**

**2**answers

### Grothendieck says: points are not mere points, but carry Galois group actions

**42**

**4**answers

### Fields with trivial automorphism group

**41**

**2**answers

### Abel and Galois (and Arnold)

**41**

**3**answers

### transcendental Galois theory

**38**

**5**answers

### Computing the Galois group of a polynomial

**38**

**2**answers

### What are the possible sets of degrees of irreducible polynomials over a field?

**37**

**1**answer

### Degree 17 number fields ramified only at 2

**36**

**2**answers

### Can the unsolvability of quintics be seen in the geometry of the icosahedron?

**36**

**3**answers

### Does the category of (algebraically closed) fields of characteristic $p$ change when $p$ changes?

**34**

**1**answer

### Is my field algebraically closed?

**34**

**1**answer

### Does any cubic polynomial become reducible through composition with some quadratic?

**32**

**3**answers

### Fundamental groups of topoi

**31**

**4**answers

### $A_5$-extension of number fields unramified everywhere

**30**

**2**answers

### Grothendieck's "La longue Marche à travers la théorie de Galois"

**30**

**3**answers

### Consequences of Shafarevich conjecture

**29**

**2**answers

### What is the dimension of the mathematical universe?

**29**

**2**answers

### Number theory textbook based on the absolute Galois group?

**29**

**0**answers

### What do dessins tell us about the absolute Galois group?

**28**

**0**answers

### On certain representations of algebraic numbers in terms of trigonometric functions

**27**

**3**answers

### Galois theory timeline

**26**

**5**answers

### Solubility of the quintic?

**26**

**2**answers

### Are there irreducible polynomials with all zeros on two concentric circles?

**26**

**4**answers

### What are traces?

**26**

**2**answers

### How to solve a quadratic equation in characteristic 2 ?

**26**

**1**answer

### The Galois group of a random polynomial

**26**

**2**answers

### Galois theory for polynomials in several variables

**26**

**1**answer

### More on "Transalgebraic Theories" (a 19th century yoga)?

**25**

**2**answers

### Profinite groups as étale fundamental groups

**25**

**4**answers

### Is the Leopoldt conjecture almost always true?

**25**

**2**answers

### Solving the cubic by "radicals" in characteristics 2 and 3

**25**

**1**answer

### Galois Group as a Sheaf

**24**

**4**answers

### Is there a Galois correspondence for ring extensions?

**24**

**4**answers

### Why do some uniform polyhedra have a "conjugate" partner?

**23**

**3**answers

### How are motives related to anabelian geometry and Galois-Teichmuller theory?

**23**

**5**answers

### Grothendieck's Galois theory without finiteness hypotheses

**23**

**5**answers

### Anabelian geometry study materials?

**23**

**1**answer

### Janelidze's Galois theory

**22**

**2**answers