Algebraic homotopy classes of rational functions

Details Algebraic homotopy classes of rational functions Algebraic homotopy classes of rational functions

2009-12-11

arxiv.org/abs/0912.2227v2

Mathematics

Algebraic Topology

30 pages; Improved the comparison between naive and motivic homotopy classes. Added one appendix

Scientific paper

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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