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- W2947565353 abstract "We investigate several interrelated foundational questions pertaining to the theory of dga's. In particular, we note that dga's give rise to a natural notion of homology. Just as abelian homology is a homotopy group of a spectrum coming from K-theory, nonabelian homology is a homotopy group of a certain limit of such spectra; we give an explicit formula for this limit --- a necessary first step (we believe) towards any explicit computations or dimension bounds. We also consider commutative comonoids in Chow motives, which we call motivic Chow coalgebras. We discuss the relationship between Chow coalgebras and dga's of smooth proper schemes. As an application of our foundational results, we prove that among schemes which are finite etale over a number field, morphisms of associated dga's are no different than morphisms of schemes. This may be regarded as a small consequence of a plausible generalization of Kim's relative unipotent section conjecture, hence as an ounce of evidence for the latter." @default.
- W2947565353 created "2019-06-07" @default.
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- W2947565353 date "2018-11-15" @default.
- W2947565353 modified "2023-10-16" @default.
- W2947565353 title "Morphisms of rational motivic homotopy types (previously titled Nonabelian motivic homology)" @default.
- W2947565353 hasPublicationYear "2018" @default.
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