A Beilinson-Bernstein theorem for twisted arithmetic differential operators on the formal flag variety

Abstract

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.

46 pages. More details have been added and proposition 3.5.3 has been corrected

References in corpus (3)

• Localization of modules for a semisimple Lie algebra in prime characteristic
• $D$-modules arithmétiques, distributions et localisation
• D^\dagger-affinity of formal models of flag varieties

Cited by in corpus (1)

• Kashiwara's theorem for twisted arithmetic differential operators