D^\dagger-affinity of formal models of flag varieties
arXiv:1501.05837
Abstract
Let G be the group of L-rational points of a connected split reductive group over a finite extension L of Q_p. We show that formal models of the algebraic flag variety X of G are D-affine for certain sheaves of arithmetic differential operators. We then introduce the category of coadmissible G-equivariant arithmetic D-modules on the system of formal models of X and prove that it is anti-equivalent to the category of admissible locally L-analytic G-representations with trivial infinitesimal character. We compute the equivariant arithmetic D-modules of certain classes of representations.
59 pages, revised version, following referees' comments. Added more details in sections three and five, corrected statements 5.2.13 (now 5.2.29) and 5.3.8 (now 5.3.12/5.3.16), some parts of sections two and four now appear in revised form in the paper arXiv:1709.00555