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arXiv · 1801.08471

Affine Grassmannians in A^1-algebraic topology

Tom Bachmann
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Abstract

Let k be a field. Denote by Spc(k)_* the unstable, pointed motivic homotopy category and by Omega_Gm: Spc(k)_* \to Spc(k)_* the Gm-loops functor. For a k-group G, denote by Gr_G the affine Grassmannian of G. If G is isotropic reductive, we provide a canonical motivic equivalence Omega_Gm G = Gr_G. If k is perfect, we use this to compute the motive M(Omega_Gm G) in DM(k, Z).

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Tom Bachmann. 2018-01-25. Affine Grassmannians in A^1-algebraic topology. https://doi.org/10.1007/s00029-019-0471-1

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