Affine Grassmannians in A1 -homotopy theory

• Tom Bachmann ^[1]
  1. [1] Massachusetts Institute of Technology

     Massachusetts Institute of Technology

     City of Cambridge, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 25, Nº. 2, 2019
• Idioma: inglés
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• Resumen

  • Let k be a field. Denote by Spc(k)∗ the unstable, pointed motivic homotopy category and by RA1ΩGm:Spc(k)∗→Spc(k)∗ the ( A1 -derived) Gm -loops functor. For a k-group G, denote by GrG the affine Grassmannian of G. If G is isotropic reductive, we provide a canonical motivic equivalence RA1ΩGmG≃GrG . We use this to compute the motive M(RA1ΩGmG)∈DM(k,Z[1/e]) .