Affine Grassmannians in A^1-algebraic topology
Algebraic Geometry
2019-03-26 v3 Algebraic Topology
K-Theory and Homology
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).
Cite
@article{arxiv.1801.08471,
title = {Affine Grassmannians in A^1-algebraic topology},
author = {Tom Bachmann},
journal= {arXiv preprint arXiv:1801.08471},
year = {2019}
}
Comments
Published version with rewritten Section 2 available at the author's webpage