On the homological interpretation of the prounipotent completion of the fundamental group

Benjamin Enriquez (IRMA); Florence Lecomte (IRMA)

On the homological interpretation of the prounipotent completion of the fundamental group

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arxiv 2105.01338 v2 pith:D4OKW77A submitted 2021-05-04 math.AT

Benjamin Enriquez (IRMA) , Florence Lecomte (IRMA) This is my paper · ORCID

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keywords fundamentalinterpretationalgebraicbeilinsoncohomologicalcompletioncomplexconstruction

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We recall the cohomological interpretation of the unipotent quotients of the fundamental groupoid of an algebraic complex variety (Beilinson, Deligne-Goncharov). We then give a construction of the resutting transition morphisms in terms of singular homology.

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The motivic fundamental groupoid at tangential basepoints
math.AG 2025-10 conditional novelty 8.0 of 10

A general motivic fundamental groupoid at tangential basepoints is constructed over any field, with Betti and de Rham realizations matching the classical fundamental torsor and periods given by regularized iterated integrals.

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