The anabelian-geometry tag has no wiki summary.

**2**

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**1**answer

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### representation of algebraic fundamental group of projective line minus three point

everyone, I want to ask is there any result in the literature
similar to the following:
Let $ X=\mathbb{P}^1\backslash \{0,1,\infty\}$, then $X$ is defined over $\mathbb{Z}$. Let $X_{\mathbb{Q}}$ ...

**4**

votes

**1**answer

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### Basics on anabelian geometry and Grothendieck's section conjecture

Even I can find similar questions and some answers on that questions, most of them are not quite unsatisfactory to me. Maybe this is a very stupid question, but there is no other place that I can ask ...

**1**

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**1**answer

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### Field of definition of a finite etale cover of an anabelian curve

Let $X$ be an anabelian curve over a number field $K$ and let $p:Y\rightarrow X$ be a finite etale cover. Then is anything known (or has anything been conjectured) about the field of definition of ...

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**2**answers

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### What conjectures in anabelian geometry are false?

Proving things suspected to be true in anabelian geometry is usually very hard. Maybe it is easier to disprove things suspected to be false?
In particular, I am interested in false generalizations of ...

**5**

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**0**answers

276 views

### discretifications of the fundamental group functor

Grothendieck calls a "discretification" of a profinite group $\hat G$, a
discrete group $G$ whose profinite completion is isomorphic to $\hat G$.
Does Grothendieck also define a notion of the ...

**16**

votes

**1**answer

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### Why does the Section Conjecture exclude curves of genus 1?

Let $X$ be an integral proper normal curve over a (perfect) field $F$, of genus $\geq 2$. One variant of Grothendieck's "section conjecture" states that the sections $G_F \rightarrow \pi_1(X)$ of the ...

**12**

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**2**answers

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### Why should the anabelian geometry conjectures be true?

I had probed friends of mine about Grothendieck's motivation for making the anabelian geometry conjectures, and they gave me the following explanation:
If $X$ is a hyperbolic curve over some field ...

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**2**answers

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### Exotic automorphisms of the fundamental group of a curve?

A while back, J. Ellenberg brought the following problem to my attention.
If $G$ is a residually finite group, let $\widehat G$ be its profinite completion.
Let $S$ be a closed surface of genus $g ...