We define a linear structure on Grothendieck’s arithmetic fundamental group of a scheme defined over a field of characteristic 0. It allows us to link the existence of sections of the Galois group to 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.
Nous définissons une structure linéaire sur le groupe fondamental arithmétique d’un schéma défini sur un corps de caractéristique 0. Cela nous permet de lier l’existence de sections du groupe de Galois vers à l’existence d’un foncteur neutre sur la catégorie qui linéarise ce dernier. Nous appliquons cette construction à une courbe affine et aux foncteurs neutres qui proviennent d’un vecteur tangent à l’infini. Nous pouvons ainsi suivre ce point rationnel dans le revêtement universel de la courbe affine.
Revised:
Accepted:
DOI: 10.5802/aif.2418
Classification: 14F05, 14L17, 18D10
Keywords: Finite connection, tensor category, tangential fiber functor
@article{AIF_2008__58_7_2381_0, author = {Esnault, H\'el\`ene and Hai, Ph\`ung H\^o}, title = {The fundamental groupoid scheme and applications}, journal = {Annales de l'Institut Fourier}, pages = {2381--2412}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {58}, number = {7}, year = {2008}, doi = {10.5802/aif.2418}, zbl = {1167.14011}, mrnumber = {2498355}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2418/} }
TY - JOUR TI - The fundamental groupoid scheme and applications JO - Annales de l'Institut Fourier PY - 2008 DA - 2008/// SP - 2381 EP - 2412 VL - 58 IS - 7 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2418/ UR - https://zbmath.org/?q=an%3A1167.14011 UR - https://www.ams.org/mathscinet-getitem?mr=2498355 UR - https://doi.org/10.5802/aif.2418 DO - 10.5802/aif.2418 LA - en ID - AIF_2008__58_7_2381_0 ER -
Esnault, Hélène; Hai, Phùng Hô. The fundamental groupoid scheme and applications. Annales de l'Institut Fourier, Volume 58 (2008) no. 7, pp. 2381-2412. doi : 10.5802/aif.2418. https://aif.centre-mersenne.org/articles/10.5802/aif.2418/
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