On $$p$$p-adic lattices and Grassmannians

  title={On \$\$p\$\$p-adic lattices and Grassmannians},
  author={Martin Kreidl},
  journal={Mathematische Zeitschrift},
  • M. Kreidl
  • Published 2 October 2010
  • Mathematics
  • Mathematische Zeitschrift
It is well-known that the coset spaces $$G(k((z)))/G(k[[z]])$$G(k((z)))/G(k[[z]]), for a reductive group $$G$$G over a field $$k$$k, carry the geometric structure of an inductive limit of projective $$k$$k-schemes. This $$k$$k-ind-scheme is known as the affine Grassmannian for $$G$$G. From the point of view of number theory it would be interesting to obtain an analogous geometric interpretation of quotients of the form $$\mathcal {G}(\mathbf {W}(k)[1/p])/\mathcal {G}(\mathbf {W}(k))$$G(W(k)[1/p… 
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