• Corpus ID: 237605086

Algebraic loop groups

@inproceedings{Rulling2021AlgebraicLG,
  title={Algebraic loop groups},
  author={Kay Rulling and Stefan Schroer},
  year={2021}
}
In this note we introduce algebraic loops, starting from the notion of an interval scheme, and define the algebraic loop group of a connected scheme with a geometric base point x0 as the set of homotopy classes of algebraic loops based at x0. The group structure is induced by concatenating algebraic loops. The main result is an isomorphism of this algebraic loop group to Grothendieck’s algebraic fundamental group for proper connected schemes over a field. 

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