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arXiv:1801.08471 [math.AG]AbstractReferencesReviewsResources

Affine Grassmannians in A^1-algebraic topology

Tom Bachmann

Published 2018-01-25Version 1

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 k is infinite and G is split reductive, we provide a canonical motivic equivalence Omega_Gm G = Gr_G. If k satisfies resolution of singularities, we use this to compute the motive M(Omega_Gm G) in DM(k, Z).

Comments: 10 pages; comments welcome!
Categories: math.AG, math.AT, math.KT
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