Esnault, Hai: The fundamental groupoid scheme and applications

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Hélène Esnault; Phùng Hô Hai
The fundamental groupoid scheme and applications
(Le groupoïde fondamental et applications)
Annales de l'institut Fourier, 58 no. 7 (2008), p. 2381-2412, doi: 10.5802/aif.2418
Article: subscription required (your ip address: 184.72.91.94) | Reviews MR 2498355 | Zbl 1167.14011
Class. Math.: 14F05, 14L17, 18D10
Keywords: Finite connection, tensor category, tangential fiber functor

Résumé - Abstract

We define a linear structure on Grothendieck’s arithmetic fundamental group $\pi _1(X, x)$ of a scheme $X$ defined over a field $k$ of characteristic 0. It allows us to link the existence of sections of the Galois group $\operatorname{Gal}(\bar{k}/k)$ to $\pi _1(X, x)$ with the existence of a neutral fiber functor on the category which linearizes it. We apply the construction to affine curves and neutral fiber functors coming from a tangent vector at a rational point at infinity, in order to follow this rational point in the universal covering of the affine curve.

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