# Galois

Ask AI3: What is Galois?

Votes:
2 promotes

## Sentences

The development of abstract algebra brought with itself group theory, rings and fields,

**Galois**theory.
Field automorphisms are important to the theory of field extensions, in particular

**Galois**extensions.
In the case of a

**Galois**extension L / K the subgroup of all automorphisms of L fixing K pointwise is called the**Galois**group of the extension.
Mordell's theorem had an ad hoc proof ; Weil began the separation of the infinite descent argument into two types of structural approach, by means of height functions for sizing rational points, and by means of

**Galois**cohomology, which was not to be clearly named as that for two more decades.
He also provided an algebraic definition of fundamental groups of schemes and more generally the main structures of a categorical

**Galois**theory.
Esquisse d ’ un Programme was published in the two-volume proceedings Geometric

**Galois**Actions ( Cambridge University Press, 1997 ).
La Longue Marche à travers la théorie de

**Galois**Long March Through**Galois**Theory is an approximately 1600-page handwritten manuscript produced by Grothendieck during the years 1980 – 1981, containing many of the ideas leading to the Esquisse d ' un programme ( see below, and also a more detailed entry ), and in particular studying the Teichmüller theory.
In that setting one can use birational geometry, techniques from number theory,

**Galois**theory and commutative algebra, and close analogues of the methods of algebraic topology, all in an integrated way.
* Artin conductor, an ideal or number associated to a representation of a

**Galois**group of a local or global field
Typical of the courses he teaches is his seminar " Group Theory and

**Galois**Theory Visualized ", in which abstract mathematical ideas are rendered as concretely as possible.
Évariste

**Galois**() ( 25 October 1811 – 31 May 1832 ) was a French mathematician born in Bourg-la-Reine.
His work laid the foundations for

**Galois**theory and group theory, two major branches of abstract algebra, and the subfield of**Galois**connections.
Page 1 of 29.
More sentences »

0.097 seconds.