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5 votes
1 answer
585 views

Reconstruction of hyperbolic curves using the fundamental group

In the paper Curves and their Fundamental Groups written by Gerd Faltings, Mochizuki's proof of Grothendick's conjecture on anabelian curves is explained. In the proof, he shows that for two ...
camilo's user avatar
  • 527
3 votes
1 answer
600 views

Grothendieck's section conjecture and base change: restricting sections

Let $X$ be a smooth projective geometrically connected curve over $\mathbf{Q}$ of genus at least two. Fix an algebraic closure $\overline{\mathbf{Q}}$ of $\mathbf{Q}$ and let $G_{\mathbf{Q}}$ be the ...
Jan Hendrik's user avatar
4 votes
1 answer
604 views

A question about the Tannakian etale fundamental group of a curve

Let $X$ be a smooth connected quasi-projective curve over $\mathbf{Q}$. Let $U$ be the pro-unipotent etale fundamental group of $X$ over $\mathbf{Q}_p$. $U^1 = U$ and let $U^n =[U,U^{n-1}]$. Let $n\...
Harry's user avatar
  • 1,213