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Algebraic homotopy classes of rational functions

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00831470
Contributor : Carole Juppin <>
Submitted on : Friday, June 7, 2013 - 10:29:07 AM
Last modification on : Monday, October 12, 2020 - 2:28:05 PM

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  • HAL Id : hal-00831470, version 1
  • ARXIV : 0912.2227

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

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