Questions tagged [anabelian-geometry]

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75 votes
1 answer
14k views

What is an étale theta function?

Let me start out by urging you to take seriously that whatever I write about the papers surrounding IUTT really are questions. If you would like to use it as a guide to the mathematics in any way, ...
Minhyong Kim's user avatar
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24 votes
5 answers
7k views

Anabelian geometry study materials?

I want to study anabelian geometry, but unfortunately I'm having difficulties in finding some materials about it. If you could offer me some books/papers/articles I would be glad.
terett's user avatar
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20 votes
2 answers
4k views

"Fermat's last theorem" and anabelian geometry?

Do I remember a remark in "Sketch of a program" or "Letter to Faltings" correctly, that acc. to Grothendieck anabelian geometry should not only enable finiteness proofs, but a proof of FLT too? If yes,...
Thomas Riepe's user avatar
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17 votes
1 answer
3k views

Why is the section conjecture important?

As in the title, I want to know the reason for importance of the section conjecture. Of course, the statement of conjecture is important as itself, even I cannot fully grasp the soul of it. However, ...
Kevin.lijh's user avatar
15 votes
0 answers
2k views

Inter-Universal Teichmuller Theory and the Field with One Element

The idea of the "field with one element", or $\mathbb{F}_{1}$, is supposed to allow us to do for number fields what we can do for function fields. Hence this idea often comes up regarding problems ...
Anton Hilado's user avatar
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13 votes
1 answer
745 views

Abelian $\ell$-adic representations in $\widehat{\mathrm{SL}(2,\mathbb{Z})}$

$\DeclareMathOperator\SL{SL}\DeclareMathOperator\Gal{Gal}\newcommand{\Z}{\mathbb{Z}}$In Grothendieck's Esquisse he claims that the action of $$\Gal(\mathbb Q)\to\text{Out}(\pi_1(M_{1,1})=\text{Out}(\...
Tian An's user avatar
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