Theoretical review demonstrates algebraic group actions on homotopy types in algebraic varieties, highlighting pathways toward constructing motivic structures.
We review some algebraic models for rational or integral homotopy types with the motivation of formalizing what it means for affine algebraic group to act on a homotopy type. We give some applications to the construction of a motivic structure on the homotopy type of algebraic varieties. This article is part of the theme issue 'Derived Lie algebras in geometry and topology'.
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Geoffroy Horel (2026) studied this question.
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