Le complémentaire d’un ensemble algébrique dans un espace projectif complexe de dimension et la trace de ce complémentaire sur un hyperplan assez général ont mêmes groupes d’homotopie jusqu’à l’ordre . Cela généralise un théorème de H. Hamm et Lê Dũng Tráng sur le complémentaire d’une hypersurface projective.
In topology, the notions of the fundamental group and the universal cover are closely intertwined. By importing usual notions from topology into the algebraic and arithmetic setting, we construct a fundamental group family from a universal cover, both of which are schemes. A geometric fiber of the fundamental group family (as a topological group) is canonically the étale fundamental group. The constructions apply to all connected quasicompact quasiseparated schemes. With different methods and hypotheses,...