| Résume | In his manuscripts from the 1980's Grothendieck proposed ideas that havebeen interpreted variously as embedding the theory of schemes into either\begin{itemize}\item group theory and higher-dimensional generalizations,\item or homotopy theory.\end{itemize}It was suggested, moreover, that such a framework would have profoundimplications for the study of Diophantine problems. In this talk, we willdiscuss mostly the little bit of progress made on this last point usingsome mildly non-abelian motives associated to hyperbolic curves. |
