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

@article{Kreidl2014OnL, title={On \$\$p\$\$p-adic lattices and Grassmannians}, author={Martin Kreidl}, journal={Mathematische Zeitschrift}, year={2014}, volume={276}, pages={859-888} }

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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