All Questions
8 questions
141
votes
0
answers
13k
views
Grothendieck-Teichmüller conjecture
(1) In "Esquisse d'un programme", Grothendieck conjectures
Grothendieck-Teichmüller conjecture: the morphism
$$
G_{\mathbb{Q}} \longrightarrow Aut(\widehat{T})
$$
is an isomorphism.
Here $...
- 3,065
3
votes
0
answers
158
views
What is the meaning of local inertia conjugation property?
In Hatcher, Allen; Lochak, Pierre; Schneps, Leila, On the Teichmüller tower of mapping class groups, J. Reine Angew. Math. 521, 1-24 (2000). ZBL0953.20030., we have:
Abstract. Let $\widehat{G T}^{1}$ ...
- 63.9k
10
votes
2
answers
496
views
Copies of topological fundamental groups inside etale fundamental groups given by different embeddings of your field into $\mathbb{C}$
Let $X$ be a smooth curve over a number field $K$ (not necessarily proper). Fix an algebraic closure $\overline{K}$ of $K$.
Let $i,i' : \overline{K}\hookrightarrow\mathbb{C}$ be two abstract ...
- 148k
9
votes
0
answers
699
views
Motivic Galois theory and Betti realizations?
Why Motivic Galois groups are defined with Betti realizations? (In fact Absolute Galois groups can be defined in this way (with Betti realizations), why they are so related?).
- 1,720
6
votes
1
answer
520
views
Correspondence between coverings and field extensions
I am self reading from Groups as Galois Group by Helmut Volklein
There is a result on page 94(section 5.4)
Let $G$ be a finite group. Let $P\subset P^{1}$ finite and $q\in P^{1}\P$. There is a ...
- 10.7k
14
votes
1
answer
1k
views
Concept of "Rigidity" in mathematics
I am reading from the book "Topics in Galois Theory" by Serre.
I came across the word "Rigidity". I am not able to understand this concept.
If I am not wrong, This term was first used by Thompson, ...
- 12.9k
-2
votes
1
answer
271
views
Any galois covering of $P^{1}$ over rationals are of the form $\mathbb{P}^1_L\to\mathbb{P}^1_\mathbb{Q}$
I recently came across the following statement,
The Galois coverings of $\mathbb{P}^1_\mathbb{Q}$ are all of the form
$$\mathbb{P}^1_L\to\mathbb{P}^1_\mathbb{Q}$$ where $L$ is a number field.
How ...
- 10.7k
0
votes
1
answer
197
views
Hurwitz's construction of simple covers
What is commonly meant by Hurwitz's construction of simple covers?
- 22.5k