A Beilinson-Bernstein theorem for twisted arithmetic differential operators on the formal flag variety
Let us suppose that $\mathbb{Q}_p$ is the field of $p$-adic numbers and $\mathbb{G}$ is a split connected reductive group scheme over $\mathbb{Z}_p$. In this work we will introduce a sheaf of twisted arithmetic differential operators on the formal flag variety of $\mathbb{G}$, associated to a general character. We will generalize the arguments of C. Huyghe and T. Schmidt, concerning the $\mathcal{D}^†$-affinity of the formal flag variety of $\mathbb{G}$, of certain sheaves of $p$-adically complete twisted arithmetic differential operators associated to an algebraic character, and the calculation of the global sections.
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