Algebraic homotopy classes of rational functions

Christophe Cazanave (1)

1 LJAD - Laboratoire Jean Alexandre Dieudonné

We compute the set of naive pointed homotopy classes of endomorphisms of the projective line P^1 over the spectrum of a field. Our computation compares well with Fabien Morel's one of the motivic pointed homotopy classes of endomorphisms of P^1: there is an a priori monoid structure on the set of naive homotopy classes such that canonical map from this monoid to group of motivic homotopy classes is a group completion.

Domaines: Topologie algébrique [math.AT]; Géométrie algébrique [math.AG]

Christophe Cazanave. Algebraic homotopy classes of rational functions. Annales Scientifiques de l'École Normale Supérieure, 2012, 45. ⟨hal-00831470⟩