Extending torsors on the punctured Spec(A_inf)

Abstract

We prove that torsors under parahoric group schemes on the punctured spectrum of Fontaine's ring $A_{\inf }$, extend to the whole spectrum. Using descent we can extend a similar result for the ring $\mathfrak{S}$ of Kisin and Pappas to full generality. Moreover, we treat similarly the case of equal characteristic. As applications we extend results of Ivanov on exactness of the loop functor and present the construction of a canonical specialization map from the $B_{\mathrm{dR}}^{+}$-affine Grassmannian to the Witt vector affine flag variety.

41 pages, improved main theorem to complete generality, added application to the loop functor, comments welcome!